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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 $36$ inches. $\newline$ Which equation can you use to find the height of the cape, $h$ ? $\newline$ Choices: $\newline$ (A) $600 = \frac{1}{2}h(24 + 36)$ $\newline$ (B) $600 = h(24 + 36)$ $\newline$ What is the height of the cape? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches $\newline$

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Area of quadrilaterals and triangles: word problems

Full solution

Q. 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

inches.

\newline

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

h

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

600 = h(24 + 36)

\newline

What is the height of the cape?

\newline

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

\newline

____ inches

\newline

Find Formula: First, we need to find the correct formula to calculate the height of the trapezoid-shaped cape. The area of a trapezoid is given by the formula $A = \frac{1}{2} \times (b_1 + b_2) \times h$ , where $b_1$ and $b_2$ are the lengths of the two bases, and $h$ is the height. Here, $b_1 = 24$ inches, $b_2 = 36$ inches, and $A = 600$ square inches.
Substitute Values: Using the formula for the area of a trapezoid, substitute the given values: $600 = \frac{1}{2} \times (24 + 36) \times h$ . This simplifies to $600 = \frac{1}{2} \times 60 \times h$ .
Solve for h: Solve for h by first multiplying $\frac{1}{2}$ by $60$ , which equals $30$ . So, the equation now is $600 = 30 \times h$ .
Isolate $h$ : Finally, divide both sides of the equation by $30$ to isolate $h$ : $h = \frac{600}{30}$ .
Calculate Height: Calculate $h$ : $600$ divided by $30$ equals $20$ . So, the height of the cape, $h$ , is $20$ inches.

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