CORRECT ANSWER WILL BE BRAINLIEST+20 POINTS!!!!! For the figures below, assume they are made of semicircles, quarter circles, and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer:

First Picture:

Area = 36pi - 72

Perimeter = 6pi + sqrt(288)

Second Picture:

Area = 576

Perimeter = 48pi + 48

Step-by-step explanation:

First Picture:

Area:

To find the area of the first picture, we need to find the are of quarter of a circle  and the area of the triangle (notice we divide by 4 for the circle cause its a quarter of a full circle) .

A of triangle = (b * h )/2 = (12^2)/2 = 72

A of quarter of circle = (r^2 * pi)/4 = (144*pi*)/4 = 36pi

If you subtract the circle by the triangle, you get the shaded area:

36pi - 72

Perimeter:

We need to find the curve and the hypotenuse of our triangle (again, since we only have a quarter of a circle we must divide our perimeter by 4).

hypotenuse = sqrt (12^2 + 12^2) = sqrt (288)

curve = (2*pi*r) / 4 = 24pi / 4 = 6pi

So if we add these, we should have the perimeter

6pi + sqrt (288)

Second Picture:

Area:

we just need to know the area of the square because the semi circles cancel out cause they have the same diameter.

square = 24 * 24 = 576

576

Perimeter:

we need the perimeter of a semicircle and the sides of the square.

semi circle = d*pi = 24pi

sides of square = 24

Now our sum is...

(semi circle ) 2 + (sides of square) 2 = answer

Because our perimeter consists of two semicircles and two sides of the square. And this gives us...

answer = (24pi) 2 + (24) 2 = 48pi + 48

48pi + 48

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