Question

A triangular prism and two nets are shown:

A right triangular prism is shown with two nets. The triangular base of the prism has height 5 inches, base 12 inches, and hypotenuse 13 inches. The length of the prism is 15 inches. Net A has 3 rectangles having dimensions 5 by 15, 15 by 12, and 15 by 13, and two triangles having legs 5 inches and 12 inches. Net B has 3 rectangles having dimensions 5 by 13, 13 by 12, and 13 by 15, and two triangles having legs 5 inches and 12 inches.

Which is the correct net of the prism and what is the surface area of the prism?

A. Net B with 420 square inches
B. Net B with 500 square inches
C. Net A with 510 square inches
D. Net A with 450 square inches

Answer 1

The answer is the option C

Net A with
`510` square inches

Explanation:

we know that

The surface area is equal to the sum of the areas of all the faces

In this problem the correct Net is the figure A

To find the surface area find the area of the
`3` rectangles plus the area of the
`2` triangles

so

Find the area of the
`3` rectangles

`A1=13*15+12*15+5*15=450\ in^(2)`

Find the area of the
`2` triangles

`A2=12*5/2+12*5/2=60\ in^(2)`

Adds the areas

`450\ in^(2)+60\ in^(2)=510\ in^(2)`