Question

8 find the area: 15 ft 25 ft a) 492.5 ft² b) 508.2 ft² c) 515.3 ft² d) 532.8 ft² e) 551.6 ft²

Explanation:

Step1: Identify component shapes

The figure is composed of a rectangle and two semi - circles (which form a full circle).

Step2: Calculate circle area

The diameter of the circle is $d = 15$ ft, so the radius $r=\frac{15}{2}=7.5$ ft. The area of a circle is $A_{circle}=\pi r^{2}=\pi\times(7.5)^{2}=\pi\times56.25\approx3.14\times56.25 = 176.625$ $ft^{2}$.

Step3: Calculate rectangle area

The rectangle has length $l = 25$ ft and width $w = 15$ ft. The area of the rectangle is $A_{rectangle}=l\times w=25\times15 = 375$ $ft^{2}$.

Step4: Calculate total area

The total area $A = A_{rectangle}+A_{circle}=375 + 176.625=492.5$ $ft^{2}$.

Answer:

A. $492.5\ ft^{2}$