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).
Accepted Solution
A:
The area of the given figure is 576 cm sq.The perimeter of the given figure is 96 cm.Step-by-step explanation:The shape consists of one semicircle and one square which is cut by a semicircle.To find Area:Find the area of semicircle= (πr^2)/2where r is the radius= diameter/2= 24/2= 12 cmArea of semicircle= π(12)(12)/2= 144π/2= 72π cm sq.Find the area of square= a^2where a is the side of square, a=24 cm.Area of the square= 24*24= 576 cm sq.To find the total area of the given figure,Area of the figure= Area of semicircle+(area of square- area of semicircle) = 72π+576-72π =576 cm sq. To find perimeter:Perimeter of semicircle= (2πr)/2 = (2*12*π)/2= 12π cmPerimeter of square= 4a =4*24 =96 cmPerimeter of the given figure= perimeter of semicircle+(perimeter of square- perimeter of semicircle) = 12π+96+12π =96 cm.