Question

A thin wire is in the form of an equilateral triangle of side 22 cm. Find the
area of a circle whose circumference is equal to the length of the wire.

Answer 1

Answer:

86.625 cm²

Step-by-step explanation:

Find the length of the wire:

Length = 11 + 11 + 11 = 33 cm

Find the radius:

Circumference = 2πr

33 = 2πr

r = 33/2π

r = 5.25 cm

Find the area:

Area = πr²

Area = π(5.25)² = 86.625 cm²

Answer: The area is 86.625 cm²

Answer 2

Answer:

Area of the circle = 346.5 cm²  

Step-by-step explanation:

Given data

A thin wire is in the form of an equilateral triangle of side 22 cm.

here we need to find area of the circle whose circumference is equals to the length of the wire

from given data side of the equilateral triangle = 22 cm

length of the wire will be equals to perimeter of the triangle

⇒  length of the wire = perimeter of equilateral triangle

                                   = 3 ( 22) = 66 cm

⇒ length of the wire  = 66 cm  

⇒ given circumference of the circle = length of the wire

                                                  2 π r   =  66

                                               2( $\frac{22}{7}$ ) r  =  66  

                                                          r =  $\frac{66(7)}{2(22)}$  

                                                          r = $\frac{3(7)}{2} = \frac{21}{2}$  

                                                          r =  10.5 cm

area of the circle  = π r²  

                               = $\frac{22}{7} (10.5)^{2}$  

                               = $\frac{22}{7} (110.25)$  

                               = 22( 15.75)    

                               = 346.5 cm²