Question

a triangular prism is shown below. which diagram is a net for this prism?

Explanation:

Step1: Recall net - properties of triangular prism

A triangular prism has two triangular faces and three rectangular faces. The rectangular faces connect the corresponding sides of the triangular faces.

Step2: Analyze the dimensions

The triangular prism has two right - angled triangular faces with legs 15 in and 20 in, and the length of the prism is 30 in. The three rectangular faces have dimensions: one with dimensions 15 in×30 in, one with dimensions 20 in×30 in, and one with dimensions (by using the Pythagorean theorem for the hypotenuse of the right - triangle base $c=\sqrt{15^{2}+20^{2}} = 25$ in) 25 in×30 in.

Step3: Match with the given nets

The correct net should have two right - angled triangles with sides 15 in and 20 in and three rectangles with appropriate side - lengths. The first net has the correct combination of two right - angled triangles and three rectangles with the right dimensions corresponding to the prism.

Answer:

The first net.