In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. $[Use π = \frac{22}{7}]$

Solution

Given: OABC is a square of side 7 cm

i.e. OA = AB = BC = OC = 7 cm

$∴$ Area of square OABC = ( side )² = 7² = 49 sq. cm.

Given, OAPC is a quadrant of a circle with centre O.

$∴$ Radius of the sector = OA = OC = 7 cm.

Sector angle = 90⁰

$∴ Area of quadrant OAPC = \frac{90^{0}}{360^{0}} x {πr}^{2} = \frac{1}{4} x \frac{22}{7} x 7 x 7 = \frac{77}{2} sq . cm . = 38.5 sq . cm . ∴ Area of shaded portion = Area of square OABC - Area of quadrant OAPC = (49 - 38.5) sq . cm . = 10.5 sq . cm .$

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

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Areas Related To Circles

In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. $[Use π = \frac{22}{7}]$

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

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NCERT Sample Papers

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Areas Related To Circles

In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. Use π = 227

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. $[Use π = \frac{22}{7}]$