XYZ is a circle with center O and a radius 7cm. Find the area of the shaded region.
Attached Figure / Diagram
A
84cm2
B
77cm2
C
38cm2
D
14cm2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\theta = 45 x 2 (∠ at center twice ∠ at \theta)
\theta = 90^\circ
Area of sector = \(\frac{\theta}{360}\) x \pir\(^2\)
= \(\frac{90}{360}\) x \(\frac{22}{7}\) x 7 x 7
= \(\frac{77}{2}\)cm\(^2\)
Area of triangle = \(\frac{1}{2}\) ab sin \theta
= \(\frac{1}{2}\) x 7 x 7 sin 90
= \(\frac{1}{2}\) x 7 x 7 x 1
= \(\frac{49}{2}\) cm\(^{2}\)
Area of shaded region = \(\frac{77}{2}\) - \(\frac{49}{2}\)
= \(\frac{28}{2}\)
= 14cm\(^2\)
Source: Myschool Past Questions Archive (Record #11107)