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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 $70$ inches long. $\newline$ Which equation can you use to find the area of the windshield, $A$ ? $\newline$ Choices: $\newline$ (A) $A = \frac{1}{2}(30)(80 + 70)$ $\newline$ (B) $A = \frac{1}{2}(80)(70 + 30)$ $\newline$ What is the area of the windshield? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ $\_\_\_\_$ square inches $\newline$

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Area of quadrilaterals and triangles: word problems

Full solution

Q. 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

inches long.

\newline

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

A

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

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

\newline

What is the area of the windshield?

\newline

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

\newline

\_\_\_\_

square inches

\newline

Identify formula: Identify the correct formula for the area of a trapezoid. The formula is $A = \frac{1}{2} \times (b_1 + b_2) \times h$ , where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height.
Choose correct option: Choose the correct option for the formula based on the given dimensions. The correct choice is $(A)A = \frac{1}{2}(30)(80 + 70)$ because it correctly places the height and sums the lengths of the bases.
Calculate area: Calculate the area using the chosen formula. Substitute the values into the formula: $A = \frac{1}{2} \times (80 + 70) \times 30 = \frac{1}{2} \times 150 \times 30 = 2250$ square inches.

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