Question

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Triangular prisms M and N are congruent. If one triangular face of prism M has area 8 in2, and the surface area of prism N is 166 in2, what is the area of one rectangular face from prism M?
A) 40 in2
B) 45 in2
C) 50 in2
D) 55 in2

Answer 1

Option C.
`50\ in^(2)`

Explanation:

In this problem I assume that the triangular base is an equilateral triangle

we know that

Triangular prisms M and N are congruent

so

If the surface area of prism N is 166 in2

then

the surface area of prism M is 166 in2 too

The surface area of the prism is equal to

`SA=2B+3C`

where

B is the area of one triangular face

C is the area of one rectangular face

In this problem we have

`SA=166\ in^(2)`

`B=8\ in^(2)`

substitute and solve for C

`166=2(8)+3C`

`3C=166-16`

`3C=150`

`C=50\ in^(2)`