Question

A triangular prism is 5 millimeters long and has a triangular face with a base of 3.6 millimeters and a height of 2.4 millimeters. The other two sides of the triangle are each 3 millimeters. What is the surface area of the triangular prism?

Answer 1

Check the picture below.

so, the prism is really just two triangles, and three rectangles.

the triangles have a base of 3.6 and a height of 2.4.

the rectangle at the bottom is a 3.6x5.

the rectangles slanted on the sides are two 3x5

so get the area of each, sum them up, and that's the area of the triangular prism.

$\bf \stackrel{triangles}{2\left( \cfrac{1}{2}\cdot 3.6\cdot 2.4 \right)}+\stackrel{bottom~rectangle}{3.6\cdot 5}+\stackrel{slanted~rectangles}{2\left(3\cdot 5 \right)}$

Answer 2

Here's the formula to find the area of a triangular prism: $SA=bh+2ls+lb$

Now, let's define the variables.

b (base) = 3.6 mm

h (height) = 2.4 mm

l (length) = 5 mm

s (side length) = 3 mm

Next, plug the values in for the variables in the formula and solve.

$SA=3.6(2.4) + 2 (5)(3) + (5)(3.6)$

$SA=8.64+30+18$

$SA=56.64$

Answer: the surface area is 56.64 millimeters

hope this helps! ps, I labeled a diagram for you