Answer:
[tex]A = \frac{Cr}{2}[/tex]
Step-by-step explanation:
Given
[tex]A = \frac{C}{4}[/tex]
Required
Describe another way to get area from circumference
Circumference C is calculated using:
[tex]C = 2\pi r[/tex]
Area, A is calculated using:
[tex]A = \pi r^2[/tex]
Using: [tex]C = 2\pi r[/tex]
Divide both sides by 2
[tex]\frac{C}{2} = \frac{2\pi r}{2}[/tex]
[tex]\frac{C}{2} = \pi r[/tex]
Multiply both sides by r
[tex]r*\frac{C}{2} = \pi r*r[/tex]
[tex]r*\frac{C}{2} = \pi r^2[/tex]
[tex]\frac{Cr}{2} = \pi r^2[/tex]
The expression on the right-hand side is the area.
So, substitute [tex]\pi r^2[/tex] for A
[tex]\frac{Cr}{2} = A[/tex]
Reorder
[tex]A = \frac{Cr}{2}[/tex]
