Question

Find the area of the irregular figure. Use 3.14 for π. Show your work. Round to the nearest tenth.

Answer 1

The area of the irregular figure is 8.1 ft² (rounded to the nearest tenth).

Explanation:

The irregular figure is made up of:

• A triangle with height 3.6 ft and base 2.8 ft.
• A semicircle with diameter 2.8 ft.

Area of the triangle

`\boxed{\begin{aligned}\sf Area\;of\;triangle&=\sf (1)/(2) * base * height\\\\&=\sf (1)/(2) * 2.8 * 3.6\\\\&=\sf 1.4 * 3.6\\\\&=\sf 5.04 \; ft^2\end{aligned}}`

Area of the semicircle

`\boxed{\begin{aligned}\sf Area \; of\;semicircle&= \sf (1)/(2) \pi r^2\\\\&= \sf (1)/(2)* 3.14 * (1.4)^2\\\\&= \sf (1)/(2)* 3.14 *1.96\\\\&= \sf 1.57 *1.96\\\\&= \sf 3.0772\; ft^2\end{aligned}}`

Area of the irregular figure

`\boxed{\begin{aligned}\sf Area \;of\;irregular\;figure&=\sf Area\;of\;triangle+ Area\;of\;semicircle\\\\&=\sf 5.04+3.0772\\\\&=\sf 8.1172\\\\&=\sf 8.1\; ft^2\;(nearest\;tenth)\end{aligned}}`

Therefore, the area of the irregular figure is 8.1 ft² rounded to the nearest tenth.