Question

ABCD is a square of side 6cm. Find the area of shaded region. See the image.

Answer 1

Answer:

12.32 cm²

Step-by-step explanation:

ABCD is a square of side 6cm. Find the area of shaded region. See the image

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

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

Answer 2

ANSWER:

${12.3}^{2}$

Hope it helps you.