In the adjoining figure ,ABCD is a square of side 6 cm. Find the area ofbthe shaded region.
Answers
Given : ABCD is a square of side 6cm.
To Find : the area of shaded region.
ABCD is a square with side = 6
Area of ABCD = 6 * 6 = 36 cm²
Radius of Arc = 6 cm
Area of BAC arc = (90/360) π (6)² = (1/4) (3.14) * 36 = 28.26 cm²
Area of ABD arc = (90/360) π (6)² = (1/4) (3.14) * 36 = 28.26 cm²
Let say intersection point of arc = P
Lets draw two straight line AP & BP = 6 cm = radius
Area of Arc APB = (60/360) * 3.14 * 6² = 18.84 cm²
Area of Arc BAP = (60/360) * 3.14 * 6² = 18.84 cm²
Area of Δ APB = (√3 / 4 ) * 6² = 15.58 cm²
Portion x is APB
Area of Portion x = Area of Arc APB + Area of Arc BAP - Area of ΔAPB
Area of Portion x = 18.84 + 18.84 - 15.58 = 22.1 cm²
Area of Shaded region = Area of BAC arc+ Area of ABD arc - 2*Area of Portion x
=> Area of Shaded region = 28.26 + 28.26 - 2*(22.1)
=> Area of Shaded region = 56.52 - 44.2
=> Area of Shaded region = 12.32 cm²
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Find the area ofbthe shaded region.
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