Question

a rectangular stained glass window is made up of identical sections. the window is 48 inches long and 36 inches wide. what is the area of the shaded triangular section?
options:
18 square inches
36 square inches
72 square inches
144 square inches

Explanation:

Step1: Find the number of small rectangles along the length and width

The length of the large rectangle is \(48\) inches and it is divided into \(3\) equal parts. So the length of each small - rectangle part \(l=\frac{48}{3} = 16\) inches.
The width of the large rectangle is \(36\) inches and it is divided into \(4\) equal parts. So the width of each small - rectangle part \(w=\frac{36}{4}=9\) inches.

Step2: Calculate the area of a small rectangle

The area of a rectangle is \(A = l\times w\). Substituting \(l = 16\) inches and \(w = 9\) inches, we get \(A_{small - rectangle}=16\times9 = 144\) square inches.

Step3: Relate the shaded triangle to the small rectangle

The shaded triangle has an area that is \(\frac{1}{8}\) of the area of the large rectangle. Also, note that the shaded triangle has an area that is \(\frac{1}{8}\) of the area of the large rectangle. Another way: observe that the shaded triangle has an area that is \(\frac{1}{2}\times\frac{1}{4}\times\) (area of a small rectangle - like unit).
Since the area of the large rectangle \(A_{large}=48\times36\) square inches. But a more straightforward way is to note that the shaded triangle has base \(b = 16\div2\) inches and height \(h=9\) inches (or vice - versa, using the properties of the divided rectangle).
Using the formula for the area of a triangle \(A=\frac{1}{2}\times b\times h\). If we consider the fact that the shaded triangle is \(\frac{1}{8}\) of the area of a \(16\times9\) (small - rectangle like unit in terms of division).
The area of the shaded triangle \(A=\frac{1}{2}\times\frac{16}{2}\times9\) (using base as half of the small - rectangle length and height as the small - rectangle width)

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Answer:

B. 36 square inches