Question

The

The shape of a garden is rectangular in the middle and semi circular
at the ends as shown in the diagram. Find the area and the perimeter
Т.
of this garden [Length of rectangle is
7m 20-(3.5 +3.59 metres).
1
DI
20 m​

Answer 1

`Area = 129.5m^2`

`Perimeter = 48m`

Explanation:

Given

See attachment

Required

Determine the area and the perimeter of the garden

Calculating Area

First, we calculate the
`area\ of\ the\ rectangle`

`A_1 = L * B`

Where:

`L = 20-(3.5 +3.5)`

`B = 7`

So:

`A_1 = (20 - (3.5 + 3.5)) * 7`

`A_1 = (20 - 7) * 7`

`A_1 = 13 * 7`

`A_1 = 91`

Next, we calculate the area of the two semi-circles.

Two semi-circles = One Circle

So:

`A_2 = \pi r^2`

Where

`r = (7)/(2)`

`A_2 = (22)/(7) * ((7)/(2))^2`

`A_2 = (22)/(7) * (49)/(4)`

`A_2 = (22)/(1) * (7)/(4)`

`A_2 = (22*7)/(4)`

`A_2 = (154)/(4)`

`A_2 = 38.5`

Area of the garden is

`Area = A_1 + A_2`

`Area = 91 + 38.5`

`Area = 129.5m^2`

Calculating Perimeter

First, we calculate the perimeter of the rectangle

But in this case, we only consider the length because the widths have been covered by the semicircles

`P_1 = 2 * L`

Where:

`L = 20-(3.5 +3.5)`

So:

`P_1 =2 * (20-(3.5 +3.5))`

`P_1 =2 * (20-7)`

`P_1 =2 * 13`

`P_1 =26`

Next, we calculate the perimeter of the two semi-circles.

Two semi-circles = One Circle

So:

`P_2 = 2\pi r`

Where

`r = (7)/(2)`

`P_2 = 2 * (22)/(7) * (7)/(2)`

`P_2 = (2 * 22 * 7)/(7 * 2)`

`P_2 = (308)/(14)`

`P_2 = 22`

Perimeter of the garden is

`Perimeter = P_1 + P_2`

`Perimeter = 26 + 22`

`Perimeter = 48m`