Question

Find the area of the BLUE highlighted region if the radius of the circle is 21 cm: 15 cm 12cm 9 cm​

Answer 1

Answer:

1332cm²

Step-by-step explanation:

First find the area of yellow portion(triangle) -

height of triangle = 12cm

base of triangle = 9cm

area of triangle = $\frac{1}{2}$ × h × b = $\frac{1}{2}$ × 12 × 9 = 54cm²

Now have to find the area of the circle -

radius of the circle = 21cm

area of circle = πr² = $\frac{22}{7}$ × 21 × 21 = 1386cm²

Lastly have to find the area of only the blue portion -

area of triangle = 54cm²

area of circle = 1386cm²

area of blue portion = 1386 - 54 = 1332cm²

Answer 2

Answer:

Hence, the area of the blue highlighted region

is = 1332 sq. cm.

Step-by-step explanation:

Ist side(a) = 12cm, 2nd side (b) = 9cm, 3rd side(c) = 15cm

Semi-perimeter of triangle(s) = (a+b+c) /2

= (12cm+9cm+15cm)/2 = 36cm/2 = 18cm.

Applying Heron's formula,

Area of triangle =√(s(s-a)(s-b)(s-c))

=√(18(18-12)(18-9)(18-15)) sq. cm

=√(18×6×9×3) sq. cm

= √2916 sq. cm

= 54 sq. cm

Radius of the circle (r) = 21cm

We know, πr^2 = (22/7× 21 × 21) sq. cm

= (22 × 3 × 21) sq. cm

= 1386 sq. cm

Area of blue highlighted region

= 1386 sq. cm - 54 sq. cm

= 1332 sq. cm