Find the area of the shaded portion in Fig. 9.45, where a square is inscribed in a circle whose radius is 7 cm.
[Hint: Four right-angled triangles joined at right angles to form a square]

Solution:

Given, radius of circle is 7 cm

The square is inscribed in a circle

We have to find the area of the shaded region.

Area of shaded region = area of circle - area of square

Area of square ABCD = 4 × area of triangle AOB

Area of triangle = 1/2 × base × height

Area of triangle AOB = 1/2 × OB × AO

= 1/2 × 7 × 7

= 49/2 cm²

Area of square ABCD = 4 × 49/2

= 2(49)

= 98 cm²

Area of circle = πr²

= (22/7)(7)²

= 22(7)

= 154 cm²

Area of shaded region = 154 - 98

= 56 cm²

Therefore, the area of the shaded region is 56 cm².

✦ Try This: Find the area of the shaded portion in Fig, where a square is inscribed in a circle whose radius is 8 cm. [Hint: Four right-angled triangles joined at right angles to form a square]

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 93

Find the area of the shaded portion in Fig. 9.45, where a square is inscribed in a circle whose radius is 7 cm. [Hint: Four right-angled triangles joined at right angles to form a square]

Summary:

The area of the shaded portion in Fig. 9.45, where a square is inscribed in a circle whose radius is 7 cm, is 56 cm².

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☛ Related Questions:

• Find the area enclosed in Fig. 9.46
• Find the area enclosed in Fig. 9.47
• Find the area enclosed in Fig. 9.48