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# In Fig. 11.13, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region

**Solution:**

Given, ABCD is a __quadrilateral__.

Arcs are drawn with radius 21 cm each with vertices A, B, C and D as centres.

We have to find the area of the shaded region.

From the figure,

Here, radius = 21 cm

__Area of sector__ = πr²θ/360°

θ_{1} + θ_{2} + θ_{3} + θ_{4} = 360°

Therefore area of shaded region = πr_{1}²θ_{1}/360° + πr_{2}²θ_{2}/360° + πr_{3}²θ_{3}/360° + πr_{4}²θ/360°

= πr²/360° (θ_{1} + θ_{2} + θ_{3} + θ_{4})

= (22/7)(21)²(360°/360°)

= (22)(3)(21)

Area of the shaded region = 1386 cm²

Therefore, the area of the shaded region is 1386 cm²

**✦ Try This:** A horse is placed for grazing inside a rectangular field 40m by 36 m and is tethered to one corner by a rope 14 m long. Over how much area can it graze?(Take π = 22/7).

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

**NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 15**

## In Fig. 11.13, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region

**Summary:**

In Fig. 11.13, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. The area of the shaded region is 1386 cm²

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