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).

Solution:- In the given figure

Side of square= 10 cm

area of square =  side x side m= 10 x 10 = 100 sq cm

Now , diameter of semi circle AOD = 2r = 10cm

⇒ radius of  semi circle AOD = 5 cm

∴ area of AOD =

similarly Area of semicircle BOC =

Area of white portion in figure 1 = area of square - [ area of semicircle BOD + area of semicircle AOD]

=

Total area of white portion in the given figure=

∴Area of Shaded portion = area of square - area of total white portion

=

So the area of shaded portion is

Now perimeter of AD(which is a semicircle) = (as perimeter of semicircle=πr)

So the perimeter of shaded region = 4×perimeter of AD=4×15.7=62.8cm

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: