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### Question Description

I need an explanation for this Mathematics question to help me study.

How do i estimate the surface area of a triangular prisim

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Triangular based prism

Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3
Area of base: ½b×h
Perimeter of base: S1+ S2 + S3

So, the formula is
Surface area= 2*(area of base) + (base perimeter)*(prism height)
Or
Surface area = bh + (S1+ S2 + S3)H
where
b=Triangle base
h=Triangle height
S1=Side 1 of triangle
S2=Side 2 of triangle
S3=Side 3 of triangle
H=Prism height

Example:
A prism have right triangle base.
The triangle sides are as following: (3 m, 4 m, 5 m)
The prism height is 10 m.
Find the surface area of the prism.

Triangle base=3 m
Triangle height=4 m
Prism height=10 m
Perimeter=(3+4+5)m=12 m
Surface area=bh + (S1+ S2 + S3)H
Surface area=3(4)+12(10) m^2
Surface area=132 m^2

Purdue University
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