A prism has a right triangle as its base with a hypotenuse that measures 5 meters and legs that measure 3 meters and 4 meters. What is the surface area of this prism if the height of the prism is 6 meters?
78 m^2
84 m^2
96 m^2
102 m^2

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- Jlastino

I suck at drawing lol so the problem says that the sides of the triangle are 5,3 and 4
and the height is 6
And we are asked to look for the surface area
If you would get the "pieces" of the prism
you would get....2 bases (which are triangles) and 3 sides (which are rectangles)
the formula for the surface area is 2B+Ph
B= area of base (triangle)
P=perimeter of base (triangle)
h=height
There are three sides given for the triangle at the base (3 and 4 as the legs) (and 5 as the hypotenuse)
In any triangle, If the side lengths are known then the area of the triangle can be calculated using heron's formula
A= sqrt (S*(S-a)(S-b)(s-c)
where s is the semi perimeter (meaning half of the perimeter)
S=(a+b+c)/2
We need to find s first
a=3
b=4
c=5
(3+4+5)/2
12/2
4
Then use that for the equation
A= sqrt (S*(S-a)(S-b)(s-c)
A=sqrt(6(6-3)((6-4)(6-5)
= sqrt ((6(3)(2)(1)
sqrt (36)
=6
B=6
Now this is the area of the base
Now we get the perimeter of the triangle and multiply it by the height
The perimeter is the sum of all the sides
P=a+b+c
=3+4+5
12
then multiply it by 6 (which is the height
12(6)
72
Now back to the equation
2B+Ph
SA=2(6) +72
Sa=12+72
=84 :D

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