62. 32. Find the area of shaded region 20 B A 1 20 C VILJ LA
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62. 32. Find the area of shaded region 20 B A 1 20 C VILJ LA
62. 32. Find the area of shaded region 20 B A 1 20 C VILJ LA
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We start by finding the area of the full quarter circle and from that subtract the area of the right angle triangle ABC and then divide it by half to obtain the required area.
The region obtained after subtracting the area of the right triangle from the area of the full quarter circle is divided symmetrically. So the shaded part should be half the area of that region.
When it's a triangle, area of the triangle=1/2×side1×side2×sin(theta)
= 1/2×(20)×(20)×(sin90) = 200 cm²
(Assuming that the units of all lengths provided is in centimetres)
Area of the quarter circle = (90/360) πr² = (1/4)×3.14×400 = (1/4)×314×4 = 314 cm²
The difference in area = 114 cm²
Required area is half of this, so = (114/2) = 57 cm².
This is the answer.