## Tutor Answer

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.

Answer:

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

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