Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

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Answer 1

`44 \text{ in}^2`

Explanation:

We can split the composite figure into multiple simpler polygons, find each polygon's area, then add the simpler polygons' areas together to get the area of the entire composite figure.

1. Area of the trapezoid (bottom section)

`A_{\text{trapezoid}} = (b_1 + b_2)/(2) \cdot h`

`A_{\text{trapezoid}} = (5 + 3)/(2) \cdot 2`

`A_{\text{trapezoid}} = (8)/(2) \cdot 2`

`A_{\text{trapezoid}} = 4 \cdot 2`

`A_{\text{trapezoid}} = 8 \text{ in}^2`

2. Area of the rectangle (middle section)

`A_{\text{rectangle}} = l \cdot w`

`A_{\text{rectangle}} = 3 \cdot 10`

`A_{\text{rectangle}} = 30 \text{ in}^2`

3. Area of the triangle (top section)

`A_{\text{triangle}} = (1)/(2) \cdot b \cdot h`

`A_{\text{triangle}} = (1)/(2) \cdot 3 \cdot 4`

`A_{\text{triangle}} = 6 \text{ in}^2`

4. Area of the entire composite figure

`A = A_{\text{trapezoid}} + A_{\text{rectangle}} + A_{\text{triangle}}`

`A = 8 \text{ in}^2 + 30 \text{ in}^2 + 6 \text{ in}^2`

`A = 44 \text{ in}^2`