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

Answer:

$Area = 41.714$$m^2$

Step-by-step 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

$A_2 = \frac{1}{2}\pi r^2$

Where

$r=\frac{6}{2} = 3$

So:

$A_2 = \frac{1}{2} *\frac{22}{7} * 3^2$

$A_2 = \frac{1}{2} *\frac{22}{7} * 9$

$A_2 = \frac{1*22*9}{2*7}$

$A_2 = \frac{198}{14}$

$A_2 = 14.143$

For the quarter circle

$A_3 = \frac{1}{4}\pi r^2$

$A_3 = \frac{1}{4} * \frac{22}{7} * 4^2$

$A_3 = \frac{22}{7} * 4$

$A_3 = \frac{88}{7}$

$A_3 = 12.571$

Total area is:

$Area = A_1 + A_2 + A_3$

$Area = 15 + 14.143 + 12.571$

$Area = 41.714$$m^2$