Question

Use the image to answer the question.

An illustration shows the net of a triangular prism. The illustration forms a shape where the small triangle is in the middle with each side being the base of three different triangles. The height of the triangle in the middle is 5 inches as shown by a dashed line and the base is 6 inches.

Use the net to find the slant height of the triangular pyramid made of equilateral triangles if its surface area is 78 in.2 .

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slant height of the triangular pyramid, we first need to find the area of the three equilateral triangles that make up the sides of the pyramid.

The area of an equilateral triangle can be calculated using the formula A = √3/4 * s^2, where s is the length of a side.

Given that the base of the triangles is 6 inches, we can calculate the side length of the equilateral triangle using the Pythagorean theorem on the right triangle formed by the dashed line (height), base, and slant height of the pyramid.

Using the Pythagorean theorem, we have:
(0.5 * 6)^2 + 5^2 = slant height^2
9 + 25 = slant height^2
34 = slant height^2
slant height ≈ √34 ≈ 5.83 inches

Therefore, the slant height of the triangular pyramid made of equilateral triangles is approximately 5.83 inches.