Question

a semicircular garden has a 7 meter wide path around it . the perimeter of garden is 360 cm square .find the area of path?

Answer 1

Given:

Width of the path around the semicircular garden = 7 m

Perimeter of the garden = 360 m

To find:

Area of the path

Solution:

Let radius of semicircular garden  =  r m

And  width of path around the garden is around 7 m as given

We know that:

perimeter of semicircle  = πr  + 2r

πr + 2r = 360

r (π + 2) = 360

Putting the value of π which is 22/7, we get:

r(22/7 + 2) = 360

r(36/7) = 360

r = 70 m

So,  Radius of garden along with path  =  70 + 7 =  77 m  

As we know that area of semi circle = πr²/2

Area of path = π*77²/2 - π*70²/2

= 9317 - 8470 = 847 m²

Therefore, the area of the path will be 847 m².

Answer 2

Answer:

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Step-by-step explanation:

perimeter of semicircle  = πr  + 2r

πr + 2r = 360

r (π + 2) = 360

r(22/7 + 2) = 360

r(36/7) = 360

r = 360*7/36

r = 70 m

So,  total Radius (garden along with path)  =  70 + 7 =  77 m  

Area of semi circle = πr²/2

Area of path = π*77²/2 - π*70²/2

                     = 22 * 77 * 77 / 2 * 7       -       22 * 70 * 70 / 2 * 7

                     = 9317   -   7700

                  = 1617 cm sq.