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

Solution:

Given, radius of circle is 7 cm

We have to find the area of a square inscribed in the circle

Given, four right angled triangles are joined at right angles to form a square.

Consider a square ABCD,

AC and BD meet at O.

AC and BD are the diameters of the circle

Radius = 7 cm

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

Therefore, the area of square is 98 cm²

✦ Try This: Find the area of a square inscribed in a circle whose radius is 5 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 92

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

Summary:

The area of a square inscribed in a circle whose radius is 7 cm, is 98 cm²

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☛ Related Questions:

• Find the area of the shaded portion in Fig. 9.45, where a square is inscribed in a circle whose radi . . . .
• Find the area enclosed in Fig. 9.46
• Find the area enclosed in Fig. 9.47