Question

in the figure 7.48 square ABCD is inscribed in the Sector 80 c u full stop the radius of Sector C dash DX Z is 20cm complete the following activity to find the area of the shaded region​

Answer 1

In the figure 7.48 square ABCD is inscribed in the Sector 80 c u full stop the radius of Sector C dash DX Z is 20cm

Side of square ABCD = radius of sector C-BXD = 20 cm

Area of square = (side)² = 20² = 400 cm²

Area of shaded region inside the square

= Area of square ABCD - Area of sector C-BXD

$= 400 - \dfrac{\theta}{360^0} \times \pi r^2\\\\= 400 - \dfrac{90^0}{360^0} \times 3.14 \times 400\\\\= 400 - 314\\\\= 86 cm^2$

Radius of bigger sector = Length of diagonal of square ABCD = 20√2 cm

Area of the shaded regions outside the square

= Area of sector A-PCQ - Area of square ABCD

= A(A-PCQ) - A(ABCD)

$= \dfrac{\theta}{360^0} \times \pi \times r^2 - 20^2\\\\= \dfrac{90^0}{360^0} \times 3.14 \times (20 \sqrt 2)^2 - 20^2\\\\= 628 - 400\\\\= 228 cm^2$

Therefore, the total surface area of the shaded region = 86 + 228 = 314cm²