Question

Now, find the area of the long rectangle along the edges of the bases. You can use the calculator to help you solve.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is 24 in2.

The area of the long rectangle is
in2.

Answer 1

To find the area of the long rectangle along the edges of the bases of the right triangular prism, we need to calculate the area of the three rectangular faces formed by the height of the prism (12 inches) and the lengths of the sides of the triangular base.

Given:
- The base of the triangular triangle measures \( 6 \) in (the base side),
- The height of the triangular base measures \( 8 \) in (the height),
- The hypotenuse of the triangular base measures \( 10 \) in (the slant side),
- The height of the prism measures \( 12 \) in.

The long rectangle consists of three rectangles corresponding to each edge of the triangular base:

1. **Rectangle corresponding to the base of the triangle:**
- Width = base of the triangle = \( 6 \) in
- Area = \( \text{width} \times \text{height} = 6 \times 12 = 72 \) in²

2. **Rectangle corresponding to the height of the triangle:**
- Width = height of the triangle = \( 8 \) in
- Area = \( \text{width} \times \text{height} = 8 \times 12 = 96 \) in²

3. **Rectangle corresponding to the hypotenuse of the triangle:**
- Width = hypotenuse of the triangle = \( 10 \) in
- Area = \( \text{width} \times \text{height} = 10 \times 12 = 120 \) in²

Now, add the areas of the three rectangles to find the total area of the long rectangle:
\[
\text{Total area} = 72 + 96 + 120 = 288 \text{ in}²
\]

Therefore, the area of the long rectangle is \( \boxed{288} \) in².