Question

Find the surface area. Round your answer to the nearest whole number.

Answer 1

143 yd²

Explanation

The surface area of the shape is composed of 2 trapezoids with bases of 3 and 7 yd and a height of 3.5 yd, 2 rectangles with dimensions 6x4 yd, 1 rectangle with dimensions 6x7 yd, and 1 rectangle with dimensions 6x3 yd.

The area of the trapezoids is calculated as follows:

`\begin{gathered} A_(trapezoid)=(base_1+base_2)/(2)\cdot height \\ A_1=(3+7)/(2)\cdot3.5 \\ A_1=5\cdot3.5 \\ A_1=17.5\text{ yd}^2 \end{gathered}`

The area of the rectangles is calculated as follows:

`\begin{gathered} A_(rectangle)=lenght\cdot width \\ A_2=6\cdot4=24\text{ yd}^2 \\ A_3=6\cdot7=42\text{ yd}^2 \\ A_4=6\cdot3=18\text{ yd}^2 \end{gathered}`

Finally, the surface area is:

`\begin{gathered} SA=2A_1+2A_2+A_3+A_4 \\ SA=2\cdot17.5+2\cdot24+42+18 \\ SA=35+48+42+18 \\ SA=143\text{ yd}^2 \end{gathered}`