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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 $10$ meters. $\newline$ Which equation can you use to find the area of the pasture, $A$ ? $\newline$ Choices: $\newline$ (A) $A = \frac{1}{2}(20)(10 + 30)$ $\newline$ (B) $A = \frac{1}{2}(10)(30 + 20)$ $\newline$ What is the area of the pasture? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ square meters $\newline$

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Area of quadrilaterals and triangles: word problems

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Q. 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

meters.

\newline

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

A

?

\newline

Choices:

\newline

(A)

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

\newline

(B)

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

\newline

What is the area of the pasture?

\newline

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

\newline

____ square meters

\newline

Identify formula: Step $1$ : Identify the correct formula to calculate the area of a trapezoid. $\newline$ The formula for the area of a trapezoid is $A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$ . Comparing this with the given choices: $\newline$ (A) $A = \frac{1}{2}(20)(10 + 30)$ - Incorrect, as it multiplies the wrong values. $\newline$ (B) $A = \frac{1}{2}(10)(30 + 20)$ - Correct, as it uses the correct formula structure.
Plug in values: Step $2$ : Plug in the values into the correct formula to calculate the area. $\newline$ Using choice (B): $\newline$ $A = \frac{1}{2} \times (30 + 20) \times 10$ $\newline$ $A = \frac{1}{2} \times 50 \times 10$ $\newline$ $A = 250$ square meters

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