Question

In the adjoining figure ,ABCD is a square of side 6 cm. Find the area ofbthe shaded region.

Answer 1

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  

Learn More:

Find the area ofbthe shaded region.

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Answer 2

Step-by-step explanation:

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