Question

I need help help with this geometry question

Answer 1

Given the a figure;

The figure is a square with the unshaded region is a semi circle.

The measure of the side lengths of the square is 25 ft

To find the area, A, of the shaded region, the formula is

`\begin{gathered} A=Area\text{ of Square}-Area\text{ of a semi circle} \\ A=(l^2)-((\pi r^2)/(2)) \end{gathered}`

Where

`\begin{gathered} l=25\text{ ft} \\ d\text{ is the diameter of the semi circle} \\ d=l=25\text{ ft} \\ r\text{ is the radius of the semi circle} \\ r=(d)/(2)=(25)/(2)=12.5\text{ ft} \\ r=12.5\text{ ft} \end{gathered}`

Substitute the values of the variables into the formula above

`\begin{gathered} A=25^2-((\pi\cdot12.5^2)/(2)) \\ A=625-245.4369 \\ A=379.5631\text{ ft}^2 \\ A=379.56\text{ ft}^2\text{ \lparen nearest hundredth\rparen} \end{gathered}`

Hence, the answer is 379.56 ft² (nearest hundredth)