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