Question

geometry module 9 DBAGeometry Module 9 DBA Be sure to show and explain all work.Part 1 ApplicationA semi-circle window can be used above a doorway or as an accent windowin a room to allow more light in large rooms. The semi-circle window in yourhome theater room lets too much light in so that the movie experience is notoptimal at any time of the day.You research and find there are "room darkening" blinds and shades forsemi-circle windows. You can't quite reach the semi-circle window tomeasure but you are able to measure the window beneath. The height of the

Answer 1

Solution

- To understand the question, we can draw a figure of the window as follows:

- The area of the figure above is simply the addition of the area of the semicircle and the area of the rectangle.

- The semicircle has a diameter of 50 inches and the rectangle has dimensions of 50 inches by 85 inches.

- Thus, we can find the area of the semicircular window as follows:

$\begin{gathered} A=A_S+A_R \\ where, \\ A_S=\text{ Area of the semicircle} \\ A_R=\text{ Area of the rectangle} \\ \\ \text{ Area of a semicircle is given by:} \\ A_S=\frac{1}{2}\pi\times(\frac{d}{2})^2\text{ \lparen}d=\text{ diameter\rparen} \\ \\ \\ \text{ Area of rectangle is given by:} \\ A_R=l\times w \\ where, \\ l=length \\ w=width \\ \\ \text{ Thus, we have:} \\ A=\frac{1}{2}\pi\times(\frac{50}{2})^{^2}+(85\times50) \\ \\ \therefore A=981.7477+4250 \\ \\ A=5231.7477in^2 \end{gathered}$

Final Answer

The area is 5231.7477square inches