Question

A rectangular stained glass window is made up of identical triangular parts as pictured below.

24 triangles are connected to have a height of 36 inches and a width of 48 inches. Every 2 triangles combine to form a rectangle.

What is the area of the shaded triangular section?
18 square inches
36 square inches
72 square inches
144 square inches

Answer 1

To determine the area of the shaded triangular section in the stained glass window, we first need to break down the information provided.

1. **Dimensions of the window**: The overall height is 36 inches and the width is 48 inches.
2. **Triangles**: The window consists of identical triangular parts, 24 in total.

Since every 2 triangles combine to form a rectangle, we can infer that there are 12 rectangles.

Now we need to calculate the area of one triangle. Each rectangle is formed by 2 triangles, so the area of one triangle will be half the area of a rectangle.

3. **Area of the entire window**:
\[
\text{Area} = \text{height} \times \text{width} = 36 \text{ inches} \times 48 \text{ inches} = 1728 \text{ square inches}
\]

4. **Area of one rectangle**:
Since there are 12 rectangles in total:
\[
\text{Area of one rectangle} = \frac{1728 \text{ square inches}}{12} = 144 \text{ square inches}
\]

5. **Area of one triangle**:
Since each rectangle is made of 2 triangles:
\[
\text{Area of one triangle} = \frac{144 \text{ square inches}}{2} = 72 \text{ square inches}
\]

So, the area of the shaded triangular section is:

\[
\boxed{72} \text{ square inches}
\]