Answer:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
Step-by-step explanation:
Given that
Area of a circle [tex]A=\pi r^2[/tex]
Circumference of the circle [tex]C = 2 \pi r[/tex]
Let us re-write the equation of area of circle:
[tex]A=\pi r^2[/tex]
[tex]A = \pi \times r \times r[/tex]
Multiplying and dividing with 2:
[tex]A = \dfrac{2\pi r}{2} \times r\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C}{2} \times r\\\text{Multiplying and dividing by } 2\pi:\\\Rightarrow A = \dfrac{C}{2} \times \dfrac{2\pi r}{2\pi}\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C \times C}{4 \pi}\\\Rightarrow A = \dfrac{C^2}{4 \pi}[/tex]
Hence, A in terms of C can be represented as:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
