Question

What is the surface area of the right triangular prism shown below. For grading purposes your answer should include only numbers.

Answer 1

Answer: $SA=189\ mm^2$

Step-by-step explanation:

You need to use the following formula for calculate the Surface area of a Right triangular prism:

$SA=ph+2B$

Where "p" is the perimeter of the base, "h" is the height of the prism and "B" is the area of the base.

You can identify that the height is:

$h=9\ mm$

The area of a triangle can be found with this formula:

$A=\frac{bH}{2}$

Where "b" is the height of the triangle and "H" is its height.

Knowing this formula, you can find the area of the base of the prism. This is:

$B=\frac{6\ mm*4.5\ mm}{2}\\\\B=13.5\ mm^2$

Since the perimeter of a figure is the sum of the lenghts of its sides, "p" is:

$p=4.5\ mm+6\ mm+7.5\ mm=18\ mm$

Therefore, substituting values into the formula, you get:

$SA=(18 mm)(9} mm)+2(13.5} mm^2)\\\\SA=189\ mm^2$