Question

Please help me on this geometry please it needs to be done ASAP with work shown it says Find the area of the shaded region

Answer 1

area of the square = 16² = 256 cm²

area of the circle =

`\pi {r}^(2) = 3.14 * {8}^(2) = 200.96 \: {cm}^(2)`

therefore area of the shaded region is:

256 - 200.96 = 55 cm²

and the closest answer is D)

Answer 2

D) 54.9 cm²

Explanation:

The diagram shows a square with a circle inside it, and the question asks us to calculate the shaded area, which is the area inside the square not taken up by the circle.

The length of the sides of the square is 16 cm, and the radius of the circle can be seen to be half of that. Therefore, the radius of the circle is 8 cm.

To calculate the area of the shaded region, we have to first calculate the area of the square and then subtract the area of the circle inside.

• Let's calculate the area of the square first:

Area = side × side

= 16 cm × 16 cm

= 256 cm²

• Now let's calculate the area of the circle:

Area = π × r²

= π × (8 cm)²

= 64π cm²

• Finally, we have to simply subtract the area of the circle from the area of the square:

area of shaded region = 256 cm² - 64π cm²

= 54.9 cm²

Therefore, the area of the shaded region is 54.9 cm², and the correct option is D.