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Answer:
[tex]Area = 41.714[/tex][tex]m^2[/tex]
Step-by-step explanation:
Given
Rectangle:
[tex]Length = 2.5m[/tex]
[tex]Width = 6m[/tex]
Semicircle
[tex]Diameter = 6m[/tex]
Quarter circle
[tex]Radius = 4m[/tex]
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:
[tex]A_1= Length * Width[/tex]
[tex]A_1= 2.5m * 6m[/tex]
[tex]A_1= 15m^2[/tex]
For the semicircle
[tex]A_2 = \frac{1}{2}\pi r^2[/tex]
Where
[tex]r=\frac{6}{2} = 3[/tex]
So:
[tex]A_2 = \frac{1}{2} *\frac{22}{7} * 3^2[/tex]
[tex]A_2 = \frac{1}{2} *\frac{22}{7} * 9[/tex]
[tex]A_2 = \frac{1*22*9}{2*7}[/tex]
[tex]A_2 = \frac{198}{14}[/tex]
[tex]A_2 = 14.143[/tex]
For the quarter circle
[tex]A_3 = \frac{1}{4}\pi r^2[/tex]
[tex]A_3 = \frac{1}{4} * \frac{22}{7} * 4^2[/tex]
[tex]A_3 = \frac{22}{7} * 4[/tex]
[tex]A_3 = \frac{88}{7}[/tex]
[tex]A_3 = 12.571[/tex]
Total area is:
[tex]Area = A_1 + A_2 + A_3[/tex]
[tex]Area = 15 + 14.143 + 12.571[/tex]
[tex]Area = 41.714[/tex][tex]m^2[/tex]