Question

In the given quadrant AOB of radius 9 cm, if

BC = OD = 3 cm. Then, find the area of the

shaded region.​

Answer 1

Step-by-step explanation:

Area of shaded region = Area of quadrant OACB - Area of A BOD We calculated Area of quadrant in part (i) Area of A BOD Area of A BOD = 2 X Base X Height %3D Since OACB is a quadrant Z BOA = 90° %

Answer 2

Given:

A quadrant AOB of radius 9 cm

BC = OD = 3 cm

To find:

Area of the shaded region in the given diagram

Solution:

To find the area of the shaded region we have to find the area of the quadrant first then subtract the area of the smaller triangle from the the quadrant we will get the required result

The radius of the quadrant is 9 cm

then the area of the quadrant is given by:

• $\frac{1}{4}\pi r^{2}$
• $\frac{1}{4}\pi 9^{2}$
• $\frac{1}{4}\frac{22}{7} r^{2}$
• $\frac{891}{14}$ cm²

we have given

BC = OD = 3 cm

so the length of

AD = 6 cm

CO = 6 cm

as we know that

in ΔAOC and ΔADE

one of the angle is 90° and one angle is common in both then the given triangle must be similar to each other,

so by the property of the similar triangles we get:

• $\frac{AD}{AO} =\frac{ED}{CO}$
• $\frac{6}{9} =\frac{ED}{6}$
• ED = 4 cm

Then the area of the ΔADE is given by:

• $\frac{1}{2} Base.Height$
• $\frac{1}{2} 6.4$
• 12 cm²

Area of the shaded portion = Area of quadrant - Area of ΔADE

• Area = $\frac{891}{14}-12$
• Area = $\frac{891-168}{14}$
• Area = $\frac{723}{14}$ cm²

Area of the shaded region is $\frac{723}{14}$ cm²