Question

a trapezoid and a semicircle compose the floorplan of a room with a curved bay window. determine the approximate amount of flooring needed to cover the room.

Explanation:

Step1: Calculate trapezoid area

The formula for the area of a trapezoid is $A_{t}=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a = 3$ yd, $b = 8$ yd, and $h = 4$ yd. So $A_{t}=\frac{(3 + 8)\times4}{2}=\frac{11\times4}{2}=22$ square yards.

Step2: Calculate semi - circle area

The formula for the area of a full - circle is $A_{c}=\pi r^{2}$, and for a semi - circle $A_{s}=\frac{1}{2}\pi r^{2}$. The diameter of the semi - circle is 3 yd, so the radius $r=\frac{3}{2}$ yd. Then $A_{s}=\frac{1}{2}\pi(\frac{3}{2})^{2}=\frac{9\pi}{8}\approx\frac{9\times3.14}{8}=\frac{28.26}{8}=3.5325$ square yards.

Step3: Calculate total area

The total area $A = A_{t}+A_{s}$. So $A=22 + 3.5325=25.5325\approx25.53$ square yards.

Answer:

Approximately 25.53 square yards of flooring is needed.