Question

Carter needs to remove sod in his yard to build three flower beds. One bed will be a rectangle which measures 2.5 m by 6 m. Another bed will be a semicircle which has a diameter of 6 m. The other bed will be a quarter circle with a radius of 4 m.

Answer 1

`Area = 41.714`
`m^2`

Explanation:

Given

Rectangle:

`Length = 2.5m`

`Width = 6m`

Semicircle

`Diameter = 6m`

Quarter circle

`Radius = 4m`

Required

The square meters of sod will Carter remove [Missing information]

To do this, we simply calculate the area of each flower beds.

For the rectangle:

`A_1= Length * Width`

`A_1= 2.5m * 6m`

`A_1= 15m^2`

For the semicircle

`A_2 = (1)/(2)\pi r^2`

Where

`r=(6)/(2) = 3`

So:

`A_2 = (1)/(2) *(22)/(7) * 3^2`

`A_2 = (1)/(2) *(22)/(7) * 9`

`A_2 = (1*22*9)/(2*7)`

`A_2 = (198)/(14)`

`A_2 = 14.143`

For the quarter circle

`A_3 = (1)/(4)\pi r^2`

`A_3 = (1)/(4) * (22)/(7) * 4^2`

`A_3 = (22)/(7) * 4`

`A_3 = (88)/(7)`

`A_3 = 12.571`

Total area is:

`Area = A_1 + A_2 + A_3`

`Area = 15 + 14.143 + 12.571`

`Area = 41.714`
`m^2`