Question

In the figure, triangle ABC in the semi circle . Find the area if the shaded region given that AB =42 cm.

Answer 1

Answer:

943.74 cm²

Step-by-step explanation:

AB= diameter = 42cm

diameter = 2 x radius = 42cm

radius = 21cm

OC = radius of circle = 21cm

area of triangle ACB = ar. of AOC + ar. of BOC

                                  = 1/2 * base * height + 1/2 * base * height

                                 = 1/2(21*21 + 21*21)

                                 = 1/2(882)

                                 = 441cm²

area of semi-circle= π*r² =  π*(d/2)² = 3.14* 21*21 = 1384.74 cm²

area of shaded region = area of semicircle - area of triangle ACB

                                     = 1384.74 - 441

                                     = 943.74 cm²

Answer 2

Given:

AB=42cm

To find:

the area of the shaded region

Solution:

AB is the diameter of the semi-circle and it is also the base of the triangle ABC.

OC is the radius of the semi-circle and it is also the height of the triangle ABC.

So,

OC=$\frac{1}{2}$AB

=$\frac{42}{2}$

=21cm

Now,

area of the shaded region = area of the semi-circle - area of the triangle

area of semi-circle=$\frac{\pi r^2}{2}$

=$\frac{22}{7}$×$21$×$21$×$\frac{1}{2}$

=11×3×21

=693$cm^2$

area of the triangle= $\frac{1}{2}$×base×height

=$\frac{1}{2}$×AB×OC

=$\frac{1}{2}$×42×21

=441$cm^2$

So the area of the shaded region=(693-441)$cm^2$

=252$cm^2$

Hence, the area of the shaded region is 252$cm^2$.