Question

a rectangular pyramid is shown below. which diagram is a net for this pyramid? what is the surface area of the rectangular pyramid? square inches

Explanation:

Step1: Identify the net of the rectangular - pyramid

A net of a rectangular - pyramid consists of a rectangle as the base and four triangles attached to the sides of the rectangle. The second diagram shows a rectangle of dimensions 10 in by 10 in as the base and four triangles with the appropriate side - lengths (7 in and 10 in) attached to the sides of the rectangle.

Step2: Calculate the surface area of the rectangular pyramid

The surface area \(SA\) of a rectangular pyramid is the sum of the area of the base \(B\) and the areas of the four triangular faces \(A_{1},A_{2},A_{3},A_{4}\).
The base is a rectangle with length \(l = 10\) in and width \(w = 10\) in, so the area of the base \(B=l\times w=10\times10 = 100\) square inches.
There are two pairs of congruent triangles.
For the first pair of triangles with base \(b_1 = 10\) in and height \(h_1=7\) in, the area of one such triangle \(A_{1}=\frac{1}{2}\times b_1\times h_1=\frac{1}{2}\times10\times7 = 35\) square inches, and the combined area of the two triangles is \(2A_{1}=2\times35 = 70\) square inches.
For the second pair of triangles with base \(b_2 = 10\) in and height \(h_2 = 7\) in, the area of one such triangle \(A_{2}=\frac{1}{2}\times b_2\times h_2=\frac{1}{2}\times10\times7=35\) square inches, and the combined area of the two triangles is \(2A_{2}=2\times35 = 70\) square inches.
The surface area \(SA=B + 2A_{1}+2A_{2}=100 + 70+70=240\) square inches.

Answer:

The net is the second diagram and the surface area is 240 square inches.