Answer: [tex]SA=189\ mm^2[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the Surface area of a Right triangular prism:
[tex]SA=ph+2B[/tex]
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:
[tex]h=9\ mm[/tex]
The area of a triangle can be found with this formula:
[tex]A=\frac{bH}{2}[/tex]
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:
[tex]B=\frac{6\ mm*4.5\ mm}{2}\\\\B=13.5\ mm^2[/tex]
Since the perimeter of a figure is the sum of the lenghts of its sides, "p" is:
[tex]p=4.5\ mm+6\ mm+7.5\ mm=18\ mm[/tex]
Therefore, substituting values into the formula, you get:
[tex]SA=(18 mm)(9} mm)+2(13.5} mm^2)\\\\SA=189\ mm^2[/tex]
