MATH SOLVE

6 months ago

Q:
# 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 14 inches. Net A has 3 rectangles having dimensions 5 by 14, 14 by 12, and 14 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 14, 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?please pick from the three answers belowNet A with 420 square inchesNet A with 480 square inchesNet B with 510 square inchesNet B with 534 square inches

Accepted Solution

A:

The net for a triangular prism consists of

2 identical triangles, here all nets have sides 5,12, and 13.

3 rectangles, all with a common dimension: the height H=14 of the prism.

Each of the 3 rectangles should have dimensions

H=14 plus one of the following:

each of 5, 12, 13 corresponding to one side of the base (triangle).

So the dimensions of the rectangles are

5x14, 12x14, 13x14

And dimensions of the triangles are

5,12 and 13.

The total surface area is therefore

(5+12+13)*14 + 2*(5*12/2)

=420+60

=480.

There is only one net that satisfies this condition.

2 identical triangles, here all nets have sides 5,12, and 13.

3 rectangles, all with a common dimension: the height H=14 of the prism.

Each of the 3 rectangles should have dimensions

H=14 plus one of the following:

each of 5, 12, 13 corresponding to one side of the base (triangle).

So the dimensions of the rectangles are

5x14, 12x14, 13x14

And dimensions of the triangles are

5,12 and 13.

The total surface area is therefore

(5+12+13)*14 + 2*(5*12/2)

=420+60

=480.

There is only one net that satisfies this condition.