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
