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The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part. Give your answer as a completely simplified exact value in terms of π (no approximations).


Number 3c

The following three shapes are based only on squares semicircles and quarter circles Find the perimeter and the area of each shaded part Give your answer as a c class=
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Answer:

Area: 16Ï€-32

Perimeter: 4Ï€ + 8sqrt(2)

Step-by-step explanation:

Area:

The shaded part plus the right triangle BCD makes a quarter circle, so you can find the area of the quarter circle minus the triangle.

For the quarter circle, the radius is 8, so the entire circle area is 64Ï€, making the quarter circle 16Ï€.

The triangle is 8*8/2 = 32.

So, the quarter circle minus the triangle, or the area, is 16Ï€-32.

Perimeter:

Again, this is a quarter circle. So, you can add the lengths of arc BD and the line segment BD.

The radius is 8, so the entire circumference is 16Ï€, making the quarter circle 4Ï€.

The hypotenuse of the right triangle will be sqrt(8*8+8*8), or 8sqrt(2).

Add and get 4Ï€ + 8sqrt(2) as your perimeter.

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