Question

a composite figure is shown. which of the following represents the total area of the figure? 44 ft² 400 ft² 440 ft² 484 ft²

Explanation:

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 8\) ft, \(b=16\) ft, and \(h = 22\) ft.

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Step2: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = bh\). The base of the parallelogram is \(16\) ft (since the top - side of the trapezoid and the parallelogram's base are part of the composite figure's structure), and the height is \(4\) ft.

$$A_{parallelogram}=16\times4 = 64\mathrm{ft}^2$$

Step3: Calculate the total area

The total area \(A=A_{trapezoid}+A_{parallelogram}\)

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Answer:

\(400\mathrm{ft}^2\)