Answer
The area of the skating rink is $\approx 2973$ ft$^{2}$
Work Step by Step
1. Find the area of the circle
Let $C =$ area of the circle
$C = \pi r^{2}$
$C = \pi (25^{2})$
$C = \pi \times (625)$
$C = 1963.49508$ ft$^{2}$
Given that a quarter of the circle is taken up by the rectangular part of the rink, that quarter part has to be subtracted from the area of the circle.
$= (1963.49...) - (1963.49... \times 0.25)$
$= (1963.49...) - (490.8738...)$ ft$^{2}$
$= 1472.6215...$ ft$^{2}$
2. Find the area of the rectangle
Let $R =$ area of the rectangle
$R = length \times width$
$R = 60 \times 25$
$R = 1500$ ft$^{2}$
3. Add up the $\frac{3}{4}$ area of the circle and the area of the rectangle $= 1500 + (1472.6215...)$
$ = 2972.621556$ ft$^{2}$
$\approx 2973$ ft$^{2}$
