Question

Wire bent to square with area 81cm2 when wire bent to semicircle what is the area of semicircle?

Answer 1

Area of Square = 81cm^2
》(side)^2 = (9cm)^2
》side = 9cm
Now, Length of wire = perimeter of Square = 4(side) = 36cm.
When bent into semicircle.
Perimeter = 36cm
》pi(r)+2(r)= 36cm
》r(pi+2)=36
》r= 36/(pi+2)
》r^2 = (36^2)/((pi+2)^2)
》pi(r^2) = pi(36^2)/((pi+2)^2)
》pi(r^2)/2 = pi(36^2)/2((pi+2)^2)
》Required area = 77cm^2

Answer 2

Given, Area of square = 81 cm²

Area of square = side x side = (side)²

let side of the square = x

So, x² = 81

x = √81

x = 9

We get side of our square as 9 cm

Since the same wire in the form of a square is bent in the shape of a semicircle, then the perimeter of both the square and the circle will be same.

Perimeter of square = 4 x side = 4a (where a is the side of the square)

Perimeter = 4 x 9 = 36 cm is the perimeter of the square

Perimeter of the square = Perimeter of the semicircle

Since it is a semicircle the perimeter would be,

1/2 the circumference of the circle + diameter of the circle

Perimeter of the circle = 36 cm

So, πr + d = 36 (where r is the radius and d is the diameter of the circle)

d = 2r

So, πr + 2r = 36

r (π + 2) = 36

r (22/7 + 2) = 36

r ((22+14) / 7) = 36

36 r = 36*7

r = 7 cm

We have our radius = 7 cm

Now area of semicircle = πr²/2

= 22/14 x 7 x 7

= 77 cm²

We got our area of semicircle as 77 cm²