Radius of larger circle, R = 7 cm

Radius of smaller circle, r = \( \dfrac{7}{2}\) cm

Height of ΔBCA = OC = 7 cm

Base of ΔBCA = AB = 14 cm

Area of ΔBCA = \( \dfrac{1}{2}\) × AB × OC = (\( \dfrac{1}{2}\))×7×14 = 49 cm^{2}

Area of larger circle = πR^{2 }= (\( \dfrac{22}{7}\))×7^{2} = 154 cm^{2}

Area of larger semicircle = \( \dfrac{154}{2}\) cm^{2 }= 77 cm^{2}

Area of smaller circle = πr^{2} = \( \dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}=\dfrac{77}{2}
\) cm^{2}

Area of the shaded region

= Area of larger circle – Area of triangle – Area of larger semicircle + Area of smaller circle

Area of the shaded region = (154-49-77+\( \dfrac{77}{2}\)) cm^{2}

= \( \dfrac{133}{2}\) cm^{2} = 66.5 cm^{2}

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

A path of width 3.5 m runs around a semicircular grassy plot whose perimeter is 72 m. Find the area of the path.