Correct Answer: Option D

Explanation

θ = 45 x 2 (∠ at center twice ∠ at θ)
θ = 90°
Area of sector = \(\frac{θ}{360}\) x πr\(^2\)
= \(\frac{90}{360}\) x \(\frac{22}{7}\) x 7 x 7
= \(\frac{77}{2}\)cm\(^2\)
Area of triangle = \(\frac{1}{2}\) ab sin θ
= \(\frac{1}{2}\) 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\(^2\)

There is an explanation video available below.

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