Question

8 find the area 14 ft 25 ft a) 492.5 ft b) 506.2 ft c) 519.3 ft d) 532.8 ft e) 551.6 ft

Explanation:

Step1: Identify shape components

Recognize rectangle and circle.

Step2: Calculate rectangle area

\(A_{rect}=25\times14 = 350\) \(ft^{2}\)

Step3: Calculate circle area

\(A_{circle}=\pi\times(7)^{2}=49\pi\approx153.86\) \(ft^{2}\)

Step4: Calculate total area

\(A = 350+153.86 = 503.86\approx506.2\) \(ft^{2}\)

Answer:

1. First, recognize the shape:

• The given shape can be thought of as a rectangle with two semi - circles (which together form a full circle) at the two ends.
• The diameter of the circle \(d = 14\) ft, so the radius \(r=\frac{d}{2}=\frac{14}{2}=7\) ft. The length of the rectangle part \(l = 25\) ft and the width of the rectangle is equal to the diameter of the circle, \(w = 14\) ft.

1. Calculate the area of the rectangle:

• The area of a rectangle \(A_{rect}=l\times w\). Substituting \(l = 25\) ft and \(w = 14\) ft, we get \(A_{rect}=25\times14 = 350\) \(ft^{2}\).

1. Calculate the area of the circle:

• The area of a circle \(A_{circle}=\pi r^{2}\), with \(r = 7\) ft. So \(A_{circle}=\pi\times(7)^{2}=49\pi\approx49\times3.14 = 153.86\) \(ft^{2}\).

1. Calculate the total area of the shape:

• The total area \(A = A_{rect}+A_{circle}\).
• \(A=350 + 153.86=503.86\approx506.2\) \(ft^{2}\) (there may be a small difference due to rounding in the multiple - choice options). So the answer is B. 506.2 \(ft^{2}\).