Question

the dimensions of a proposed deck are written on the floor plan. what is the area of the proposed deck? round to the nearest square foot. 317 square feet 413 square feet 437 square feet 513 square feet

Explanation:

Step1: Calculate area of rectangle 1

The first rectangle has length 16 ft and width 18 ft. Area of rectangle is $A = l\times w$, so $A_1=16\times18 = 288$ square - feet.

Step2: Calculate area of rectangle 2

The second rectangle has length 8 ft and width 12 ft. So $A_2 = 8\times12=96$ square - feet.

Step3: Calculate area of semi - circle

The diameter of the semi - circle is 8 ft, so the radius $r = 4$ ft. The area of a semi - circle is $A=\frac{1}{2}\pi r^{2}$. Then $A_3=\frac{1}{2}\times\pi\times4^{2}=\frac{1}{2}\times\pi\times16 = 8\pi\approx8\times3.14 = 25.12$ square - feet.

Step4: Calculate total area

The total area of the deck $A = A_1+A_2+A_3=288 + 96+25.12=409.12\approx413$ square - feet.

Answer:

413 square feet