Resources

Resources

Area of quadrilaterals and triangles: word problems

Find the perimeter of the rectangle.

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9

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Use the formula:

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\begin{array}{c} p=2 \|+2 w \\ \text { perimeter }=2 \times \\ \text { length }+2 \times \text { width } \\ 1=9 \\ w=18 \\ p=[?] \end{array}

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=2 x

+2 \times

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The Oak View Middle School cheer squad made a banner to bring out for a football game against their school's biggest rival. The banner is shaped like a triangle with an area of

20

square feet. The banner is

4

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Which equation can you use to find the length of the banner's base,

b

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(A) 20 = \frac{1}{2}b(4)

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(B) 20 = 4b

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What is the length of the banner's base?

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Write your answer as a whole number or decimal. Do not round.

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\_\_\_

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Felix and his friends attended the opening of the new community center at Forest Ridge Park. The mayor unveiled a parallelogram-shaped decorative plaque at the entrance to the park with the date of the special event. Its bottom edge is

9

inches long, and its area is

126

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Which equation can you use to find how tall the plaque is,

h

\newline

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126 = \frac{1}{2} \times 9 \times h

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126 = 9h

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How tall is the plaque?

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Write your answer as a whole number or decimal. Do not round.

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The attic of Lillian's house has a large window in the shape of a triangle. The window is

8

feet long and has an area of

36

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Which equation can you use to find how tall the window is,

h

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36 = \frac{1}{2}(8)h

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36 = 8h

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How tall is the window?

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Write your answer as a whole number or decimal. Do not round.

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The River Rock Horse Rescue has a fenced-off pasture in the shape of a trapezoid. They need to calculate the area of the trapezoid to see how many horses it will safely hold. The bases of the trapezoid are

30

meters long and

20

meters long. The height of the trapezoid is

10

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Which equation can you use to find the area of the pasture,

A

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A = \frac{1}{2}(20)(10 + 30)

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A = \frac{1}{2}(10)(30 + 20)

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What is the area of the pasture?

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Write your answer as a whole number or decimal. Do not round.

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____ square meters

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Regan has been saving her allowance for months, and she finally has enough to buy a new flat-screen TV! The TV's screen is shaped like a rectangle that is

50

inches wide. The screen's area is

1,500

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Which equation can you use to find the height of the screen,

h

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1,500 = 50h

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1,500 = \frac{1}{2}(50)h

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What is the height of the screen?

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Write your answer as a whole number or decimal. Do not round.

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The base of a parallelogram is

24

feet long, and its height is

12

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Which equation can you use to find the area of the parallelogram,

A

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24 = 12 \times A

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A = 24 \times 12

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What is the area of the parallelogram?

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Write your answer as a whole number or decimal. Do not round.

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____ square feet

Becky is making a spice shelf in the shape of a triangle to fit in the corner of her kitchen cabinet. The triangle's base is

16

inches long, and its area is

96

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Which equation can you use to find the triangle's height,

h

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96 = \frac{1}{2}(16)h

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96 = 2(16)h

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What is the triangle's height?

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Write your answer as a whole number or decimal. Do not round.

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The attic of Lillian's house has a large window in the shape of a triangle. The window is

8

feet long and has an area of

36

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Which equation can you use to find how tall the window is,

h

\newline

\newline

36 = 8h

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36 = \frac{1}{2}(8)h

\newline

How tall is the window?

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Write your answer as a whole number or decimal. Do not round.

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A triangle has an area of

52\,\text{square inches}

and a height of

8\,\text{inches}

. Which equation can you use to find the length of the triangle's base,

b

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52 = \frac{1}{2}b(8 + 8)

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52 = \frac{1}{2}b(8)

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What is the length of the triangle's base?

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Write your answer as a whole number or decimal. Do not round.

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A rock cracked the windshield of Harry's truck. To get an estimate of the replacement cost, he needs to calculate the area of the windshield. The windshield is shaped like a trapezoid with a height of

30

inches. The top of the windshield is

80

inches long, and the bottom is

70

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Which equation can you use to find the area of the windshield,

A

\newline

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A = \frac{1}{2}(30)(80 + 70)

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A = \frac{1}{2}(80)(70 + 30)

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What is the area of the windshield?

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Write your answer as a whole number or decimal. Do not round.

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\_\_\_\_

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A triangle has an area of

52

square inches and a height of

8

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Which equation can you use to find the length of the triangle's base,

b

\newline

\newline

52 = \frac{1}{2}b(8)

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52 = \frac{1}{2}b(8 + 8)

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What is the length of the triangle's base?

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Write your answer as a whole number or decimal. Do not round.

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The base of a parallelogram is

24

feet long, and its height is

12

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Which equation can you use to find the area of the parallelogram,

A

\newline

\newline

A = 24 \times 12

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24 = 12 \times A

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What is the area of the parallelogram?

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Write your answer as a whole number or decimal. Do not round.

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____ square feet

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Emily's younger brother, Kenny, begged her to make him a superhero costume for Halloween this year, so of course Emily did! Emily sewed a

600

-square-inch trapezoid-shaped cape with a big ＂K＂ on it. The length along the top of the cape was

24

inches, and the length along the bottom was

36

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Which equation can you use to find the height of the cape,

h

\newline

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600 = \frac{1}{2}h(24 + 36)

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600 = h(24 + 36)

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What is the height of the cape?

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Write your answer as a whole number or decimal. Do not round.

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Toby and his dad can't wait to take their sailboat, Splash Dancer, out on the water this year! The boat's sail is shaped like a triangle. The bottom edge of the sail is

12

feet long, and the sail is

14

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Which equation can you use to find the area of the sail,

A

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A = \frac{1}{2}(12)(14)

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A = (12)(14)

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What is the area of the sail?

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Write your answer as a whole number or decimal. Do not round.

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____ square feet

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Kimi bought a trapezoidal rug as the finishing touch to her newly redecorated living room. The trapezoid has an area of

72

square feet. Its bases are

14

10

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Which equation can you use to find the trapezoid's height,

h

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72 = \frac{1}{2}h(14 + 10)

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72 = 2h(14 + 10)

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What is the trapezoid's height?

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Write your answer as a whole number or decimal. Do not round.

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\_\_\_

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The Oak View Middle School cheer squad made a banner to bring out for a football game against their school's biggest rival. The banner is shaped like a triangle with an area of

20

square feet. The banner is

4

\newline

Which equation can you use to find the length of the banner's base,

b

\newline

\newline

20 = 4b

\newline

20 = \frac{1}{2}b(4)

\newline

What is the length of the banner's base?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

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Mitch is buying a new triangular protective pad for his computer desk and needs to order the right size. The base of the triangle is

42

inches long, and its height is

20

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Which equation can you use to find the area of the pad,

A

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A = \frac{1}{2}(42)(20)

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A = \frac{1}{2}(42 + 20)

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What is the area of the pad?

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Write your answer as a whole number or decimal. Do not round.

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____ square inches

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Tanvi and her grandfather bought a vintage chess board to play chess together on the weekends. The chess board is shaped like a square, and its sides are

16

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Which equation can you use to find the area of the chess board,

A

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A = 16 + 16

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A = 16 \times 16

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What is the area of the chess board?

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Write your answer as a whole number or decimal. Do not round.

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____ square inches

To make his house more energy-efficient, Ernest is putting solar film on the large trapezoid-shaped window in his living room. The window has an area of

25

square feet. The top of the window is

3

feet long, and the bottom is

7

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Which equation can you use to find how tall the window is,

h

\newline

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25 = h(3 + 7)

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25 = \frac{1}{2}h(3 + 7)

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How tall is the window?

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Write your answer as a whole number or decimal. Do not round.

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\newline

Tanvi and her grandfather bought a vintage chess board to play chess together on the weekends. The chess board is shaped like a square, and its sides are

16

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Which equation can you use to find the area of the chess board,

A

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A) A = 16 \times 16

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B) A = 16 + 16

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What is the area of the chess board?

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Write your answer as a whole number or decimal. Do not round.

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\_\_\_\_

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Sharon is painting on a rectangular canvas. The canvas is

12

inches wide and has an area of

192

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Which equation can you use to find the height of the canvas,

h

\newline

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192 = 12h

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192 = \frac{1}{2}(12)h

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What is the height of the canvas?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

\newline

Felix and his friends attended the opening of the new community center at Forest Ridge Park. The mayor unveiled a parallelogram-shaped decorative plaque at the entrance to the park with the date of the special event. Its bottom edge is

9

inches long, and its area is

126

\newline

Which equation can you use to find how tall the plaque is,

h

\newline

\newline

126 = 9h

\newline

126 = \frac{1}{2} \times 9 \times h

\newline

How tall is the plaque?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

Becky is making a spice shelf in the shape of a triangle to fit in the corner of her kitchen cabinet. The triangle's base is

16

inches long, and its area is

96

\newline

Which equation can you use to find the triangle's height,

h

\newline

\newline

96 = 2(16)h

\newline

96 = \frac{1}{2}(16)h

\newline

What is the triangle's height?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

To make his house more energy-efficient, Ernest is putting solar film on the large trapezoid-shaped window in his living room. The window has an area of

25

square feet. The top of the window is

3

feet long, and the bottom is

7

\newline

Which equation can you use to find how tall the window is,

h

\newline

\newline

25 = \frac{1}{2}h(3 + 7)

\newline

25 = h(3 + 7)

\newline

How tall is the window?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

\newline

Tristan and his friends made a banner for their back-to-school dance. The banner is rectangular, and it is

15

5

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Which equation can you use to find the banner's area,

A

\newline

\newline

A = 15 \times 5

\newline

15 = 5 \times A

\newline

What is the area of the banner?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ square feet

The River Rock Horse Rescue has a fenced-off pasture in the shape of a trapezoid. They need to calculate the area of the trapezoid to see how many horses it will safely hold. The bases of the trapezoid are

30\,\text{meters}

20\,\text{meters}

long. The height of the trapezoid is

10\,\text{meters}

. Which equation can you use to find the area of the pasture,

A

\newline

\newline

A = \frac{1}{2}(10)(30 + 20)

\newline

A = \frac{1}{2}(20)(10 + 30)

\newline

What is the area of the pasture?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ square meters

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Tristan and his friends made a banner for their back-to-school dance. The banner is rectangular, and it is

15

5

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Which equation can you use to find the banner's area,

A

\newline

\newline

15 = 5 \times A

\newline

A = 15 \times 5

\newline

What is the area of the banner?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ square feet

The area of a rectangle is

15.6

square inches. The area of a parallelogram is

15 \frac{3}{4}

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Which shape has a greater area?

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(B) parallelogram

Brody drew two adjacent angles that form a right angle. The measure of one of the angles is

43^\circ

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m

represent the measure of the second angle. Which equation models the problem?

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\newline

43 + m = 90

\newline

m - 43 = 90

\newline

Solve this equation to find the measure of the second angle.

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^\circ

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is

18 \pi \text{ meters}

. What is the area

\newline

A

of the cross section of the column? Give your answer in terms of

\pi

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A=\square

What is the sign of

c\div d

c > 0

d < 0

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1

\newline

\newline

\newline

\newline

Find the area of a circle with a radius of

0

8

inches. Use the fact that the area of a circle is given by

A=\pi r^{2}

\pi \approx 3.14

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The area of the circle is approximately

\square

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(Simplify your answer. Type an integer or decimal rounded to four decimal places as needed.)

How wide is a rectangular strip of land with a length

\frac{1}{3}

\frac{3}{5}

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\int_{\epsilon}\sqrt{x^{2}+y^{2}+z^{2}} dV

\newline

E

lies above the cone

\newline

z=\sqrt{x^{2}+y^{2}}

and between the spheres

\newline

x^{2}+y^{2}+z^{2}=1

\newline

x^{2}+y^{2}+z^{2}=64

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The area of a circle is increasing at a rate of

8 \pi

square meters per hour.

\newline

At a certain instant, the area is

36 \pi

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What is the rate of change of the circumference of the circle at that instant (in meters per hour)?

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1

\newline

4 \sqrt{2}

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12 \pi

\newline

\frac{\pi}{6}

\newline

\frac{4 \pi}{3}

The surface area of a cube is increasing at a rate of

15

square meters per hour.

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At a certain instant, the surface area is

24

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What is the rate of change of the volume of the cube at that instant (in cubic meters per hour)?

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1

\newline

\frac{15}{2}

\newline

(\sqrt{15})^{3}

\newline

\frac{5}{8}

\newline

8

The volume of a cube is increasing at a rate of

18

cubic meters per hour.

\newline

At a certain instant, the volume is

8

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What is the rate of change of the surface area of the cube at that instant (in square meters per hour)?

\newline

1

\newline

\frac{3}{2}

\newline

24

\newline

36

\newline

(\sqrt[3]{18})^{2}

The circumference of a circle is increasing at a rate of

\frac{\pi}{2}

meters per hour.

\newline

At a certain instant, the circumference is

12 \pi

\newline

What is the rate of change of the area of the circle at that instant (in square meters per hour)?

\newline

1

\newline

\frac{\pi}{4}

\newline

36 \pi

\newline

3 \pi

\newline

6

The radius of the base of a cylinder is increasing at a rate of

1

meter per hour and the height of the cylinder is decreasing at a rate of

4

meters per hour.

\newline

At a certain instant, the base radius is

5

meters and the height is

8

\newline

What is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?

\newline

1

\newline

180 \pi

\newline

20 \pi

\newline

-20 \pi

\newline

-180 \pi

\newline

The volume of a cylinder with base radius

r

h

\pi r^{2} h

One diagonal of a rhombus is decreasing at a rate of

7

centimeters per minute and the other diagonal of the rhombus is increasing at a rate of

10

centimeters per minute.

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At a certain instant, the decreasing diagonal is

4

centimeters and the increasing diagonal is

6

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What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?

\newline

1

\newline

-1

\newline

\mathbf{1 6}

\newline

-16

\newline

1

\newline

The area of a rhombus with diagonals

d_{1}

d_{2}

\frac{d_{1} d_{2}}{2}

The area of a square is increasing at a rate of

20

square meters per hour.

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At a certain instant, the area is

49

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What is the rate of change of the perimeter of the square at that instant (in meters per hour)?

\newline

1

\newline

\frac{40}{7}

\newline

2 \sqrt{5}

\newline

28

\newline

7

The side length of a square is increasing at a rate of

15

millimeters per second.

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At a certain instant, the side length is

22

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What is the rate of change of the area of the square at that instant (in square millimeters per second)?

\newline

1

\newline

660

\newline

484

\newline

30

\newline

225

The radius of a circle is decreasing at a rate of

6

5

meters per minute.

\newline

At a certain instant, the radius is

12

\newline

What is the rate of change of the area of the circle at that instant (in square meters per minute)?

\newline

1

\newline

-156 \pi

\newline

-144 \pi

\newline

-288 \pi

\newline

-42.25 \pi

The radius of a circle is increasing at a rate of

3

centimeters per second.

\newline

At a certain instant, the radius is

8

\newline

What is the rate of change of the area of the circle at that instant (in square centimeters per second)?

\newline

1

\newline

48 \pi

\newline

9 \pi

\newline

64 \pi

\newline

192 \pi

The radius of a sphere is increasing at a rate of

7

5

meters per minute.

\newline

At a certain instant, the radius is

5

\newline

What is the rate of change of the surface area of the sphere at that instant (in square meters per minute)?

\newline

1

\newline

330 \pi

\newline

100 \pi

\newline

300 \pi

\newline

225 \pi

\newline

The surface area of a sphere with radius

r

4 \pi r^{2}

The area of a circle is increasing at a rate of

8 \pi

square meters per hour.

\newline

At a certain instant, the area is

36 \pi

\newline

What is the rate of change of the circumference of the circle at that instant (in meters per hour)?

\newline

1

\newline

12 \pi

\newline

\frac{\pi}{6}

\newline

4 \sqrt{2}

\newline

\frac{4 \pi}{3}

The radius of the base of a cylinder is increasing at a rate of

1

meter per hour and the height of the cylinder is decreasing at a rate of

4

meters per hour.

\newline

At a certain instant, the base radius is

5

meters and the height is

8

\newline

What is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?

\newline

1

\newline

-20 \pi

\newline

-180 \pi

\newline

20 \pi

\newline

180 \pi

\newline

The volume of a cylinder with base radius

r

h

\pi r^{2} h

The surface area of a sphere is increasing at a rate of

14 \pi

square meters per hour.

\newline

At a certain instant, the surface area is

36 \pi

\newline

What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)?

\newline

1

\newline

36 \pi

\newline

(\sqrt{14 \pi})^{3}

\newline

21 \pi

\newline

\frac{7}{12}

\newline

The surface area of a sphere with radius

r

4 \pi r^{2}

\newline

The volume of a sphere with radius

r

\frac{4}{3} \pi r^{3}

The radius of a circle is decreasing at a rate of

6

5

meters per minute.

\newline

At a certain instant, the radius is

12

\newline

What is the rate of change of the area of the circle at that instant (in square meters per minute)?

\newline

1

\newline

-288 \pi

\newline

-156 \pi

\newline

-42.25 \pi

\newline

-144 \pi