Question

Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.

Answer 1

Area of shaded part = 41.09733550

Perimeter of shaded part = 35.82011867

Explanation:

Area of shaded part = ((πr^2) 4) - (bh ÷ 2)

Area of shaded part = ((π(12)^2) ÷ 4) - ((12)(12) ÷ 2)

Area of shaded part = (452.3893421 ÷ 4) - (144 ÷ 2)

Area of shaded part = (113.0973355) - (72)

Area of shaded part = 41.09733550

Perimeter of shadedpart:

AC = √a^2 + b^2

AC = √12^2 + 12^2

AC = √144 + 144

AC = √288

AC = 16.97056275

Perimeter of whole circle ÷ 4:

C=2πr

C=2π(12)

C=75.39822369

C ÷ 4 = 75.39822369 ÷ 4

C ÷ 4 = 18.84955592

Perimeter of shaded part:

18.84955592 + 16.97056275 = 35.82011867