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°

θ₁ + θ₂ + θ₃ + θ₄ = 360°

Therefore area of shaded region = πr₁²θ₁/360° + πr₂²θ₂/360° + πr₃²θ₃/360° + πr₄²θ/360°

= πr²/360° (θ₁ + θ₂ + θ₃ + θ₄)

= (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

☛ Related Questions:

• A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at . . . .
• A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the cor . . . .
• With the vertices A, B and C of a triangle ABC as centres, arcs are drawn with radii 5 cm each as sh . . . .