Mathematics

XYZ is a circle with center O and a radius 7cm. Find the area of the…

XYZ is a circle with center O and a radius 7cm. Find the area of the shaded region. 

  • A.
    84cm2
  • B.
    77cm2
  • C.
    38cm2
  • D.
    14cm2
Correct Answer: Option D
Explanation

θ = 45 x 2 (∠ at center twice ∠ at θ)
θ = 90°
Area of sector = θ/360 x πr2
= 90/360 x 22/7 x 7 x 7
= 77/2cm(^2)
Area of triangle = 1/2 ab sin θ
= 1/2 x 7 x 7 sin 90
= 1/2 x 7 x 7 x 1
= 49/2 cm(^{2})
Area of shaded region = 77/2 – 49/2

= 28/2
= 14cm(^2)