Question

John is putting a fence around his garden that is shaped like a half circle and a rectangle.
A rectangle has a length of 14 feet and width of 7 feet. A semicircle with diameter of 7 feet is on top of the rectangle.
How much fencing will John need? Use StartFraction 22 over 7 EndFraction for Pi.

Answer 1

Given :

The shape of the John's garden is like a semicircle on top of a rectangle .

Length of the rectangle = 14 feet

Width of the rectangle = 7 feet

Diameter of the semicircle = 7 feet

To Find :

The amount of fencing required for the garden = ?

Solution :

Here basically we have to find the perimeter of the garden .

The shape of the garden is shown in the attached fig .

Now the perimeter of this garden will be given as :

P = circumference of the semicircle ( excluding diameter ) + perimeter of rectangle (excluding one width which is also the diameter of the semicircle )

So, P = $\pi R +( 2 \times l) + b$

Here , R is radius of the semicircle , l is length of rectangle and b is breadth or width of the rectangle

So, P = $\frac{22}{7}\times \frac{7}{2} + (2 \times 14 ) + 7$ feet      ( since R = half of diameter )

Or, P =  11 + 28 +7 feet

Or , P = 46 feet

So, the fencing required is 46 feet .