# In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region

**Solution:**

Given, arcs are drawn with radii 14 cm each with centres P, Q and R.

We have to find the area of the shaded region.

Here, radius = 14 cm

__Area of sector__ = πr²θ/360°

θ_{1} + θ_{2} + θ_{3} = 180°

Therefore area of shaded region = πr_{1}²θ_{1}/360° + πr_{2}²θ_{2}/360° + πr_{3}²θ_{3}/360°

Where r_{1} = r_{2} = r_{3} = 14

area of shaded region = πr²/360° ( θ_{1} + θ_{2} + θ_{3})

= (22/7)(14)²(180°/360°)

= (22)(2)(14)(1/2)

= (22)(14)

= 308 cm²

Area of shaded region = 308 cm²

Therefore, the area of the shaded region is 308 cm²

**✦ Try This:** A horse is tied to a pole at one corner of a square grass field of side 15 m using 10 m long rope. Find the area of that part of the field in which the horse can graze.

Given, square grass field of side 15 m

A horse is tied at one corner of the field using 10 m long rope.

We have to find the area of the field which the horse can gaze.

The area of field in which the cow gaze represents the area of a sector of a circle.

Here, radius = 10 m and corresponding angle, θ = 90°

Area of sector = πr²θ/360°

= (22/7)(10)²(90°/360°)

= (22/7)(100)(1/4)

= (22/7)(25)

= 78.57 square m

Therefore, the area of the field in which the horse can gaze is 78.57 square m.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 13**

## In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region

**Summary:**

In Fig. 11.12, arcs have been drawn with radii 14 cm each and with centres P, Q and R. The area of the shaded region is 308 cm²

**☛ Related Questions:**

- A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area . . . .
- In Fig. 11.13, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilatera . . . .
- A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at . . . .

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