189k views
3 votes
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.

If a measures 16 cm, b measures 8 cm, and d measures 17 cm, what is the surface area of the rectangular pyramid?

User Rayan Ral
by
8.1k points

1 Answer

4 votes
To find the surface area of the rectangular pyramid, we need to calculate the area of each face and then sum them up.

Looking at the net, we can see that the rectangular pyramid has one rectangular base and four triangular faces.

The dimensions of the rectangular base are a = 16 cm and b = 8 cm, so the area of the rectangular base is A_base = a * b.

The dimensions of the triangular faces are given by the sides of the rectangle and the slant height of the pyramid, which is represented by d = 17 cm. Each triangular face has a base equal to one side of the rectangle and a height equal to d.

The area of each triangular face can be calculated as A_triangle = 0.5 * (base * height) = 0.5 * (a * d) or 0.5 * (b * d).

Since there are four triangular faces, the total area of the triangular faces is A_triangles = 4 * A_triangle.

Finally, the surface area of the rectangular pyramid is the sum of the area of the rectangular base and the area of the triangular faces:

Surface Area = A_base + A_triangles = A_base + 4 * A_triangle.

Substituting the given values:

A_base = 16 cm * 8 cm = 128 cm².

A_triangle = 0.5 * (16 cm * 17 cm) = 136 cm².

A_triangles = 4 * 136 cm² = 544 cm².

Surface Area = 128 cm² + 544 cm² = 672 cm².

Therefore, the surface area of the rectangular pyramid is 672 cm².

I hope this helps! :)
User WPFNewbie
by
8.0k points

No related questions found