In Fig. ABC is a right angled triangle in which $∠ A = 90^{\circ}$ , AB = 21 cm and AC = 28 cm. Semi - circles are described on AB, BC and AC as diameters. Find the area if the shaded region.

Open in App

Solution

In right ΔABC, by Pythagoras theorem:

$B C^{2} = A B^{2} + A C^{2}$

$B C^{2} = 21^{2} + 28^{2}$

$B C^{2} = 35^{2}$

$B C = 35 c m$

$A r e a o f △ A B C = \frac{A B \times A C}{2} = \frac{21 \times 28}{2} = 294 c m^{2}$

Area of Semicircle of diameter BC = $\frac{1}{2} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} = 481.25 c m^{2}$

Area of Semicircle of diameter AB = $\frac{1}{2} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} = 173.25 c m^{2}$

Area of Semicircle of diameter AC = $\frac{1}{2} \times \frac{22}{7} \times \frac{28}{2} \times \frac{28}{2} = 308 c m^{2}$

Area of the shaded region
= Area of Semicircle of diameter AB + Area of Semicircle of diameter AC + Area of ΔABC - Area of Semicircle of diameter BC
= 173.25 + 308 + 294 - 481.25 = 294 $c m^{2}$

Suggest Corrections

Similar questions

In Fig. ABC is a right angled triangle in which $∠ A = 90^{\circ}$ , AB = 21 cm and AC = 28 cm. Semi - circles are described on AB, BC and AC as diameters. Find the area if the shaded region.

A B C

is a right-angled triangle in which

∠ A = 90^{\circ}

A B = 21 c m

and

A C = 28 c m

. Semi-circles are described on

A B, B C

, and

A C

as diameters. Find the area of the shaded region.

Q. In the following figure, ABC is a right angled triangle in which ∠A = 90°, AB = 21 cm and AC = 28 cm. Semi-circles are described on AB, BC and AC as diameters. Find the area of the shaded region.

Q. In the fig., ABC is a right-angled triangle,

∠

B = 90

^{o}

, AB = 28 cm and BC = 21 cm. With AC as diameter, a semi-circle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region.

Q. In the given figure,

△ A B C

is right-angled at

A

. Semi circles are drawn on

A B, A C

and

B C

as diameters. It is given that

A B = 3 c m

and

A C = 4 c m

. Find the area of the shaded region in

c m^{2}

Join BYJU'S Learning Program

In Fig. ABC is a right angled triangle in which ∠A=90∘, AB = 21 cm and AC = 28 cm. Semi - circles are described on AB, BC and AC as diameters. Find the area if the shaded region.

In Fig. ABC is a right angled triangle in which $∠ A = 90^{\circ}$ , AB = 21 cm and AC = 28 cm. Semi - circles are described on AB, BC and AC as diameters. Find the area if the shaded region.