SOLUTION: For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 6 m, and 7 m. The altitude is 9 m. Find the total area (in square meters) of the prism.

Algebra ->  Formulas -> SOLUTION: For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 6 m, and 7 m. The altitude is 9 m. Find the total area (in square meters) of the prism.       Log On


   

Question 1194250: For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 6 m, and 7 m. The altitude is 9 m.
Find the total area (in square meters) of the prism. (Round your answer to three decimal places.)
Find the volume (in cubic meters) of the prism. (Round your answer to three decimal places.)
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given: a=4m, b=6m, 7m, and h=9m

Find the total area (in square meters) of the prism. (Round your answer to three decimal places.)
Total Surface Area of a Triangular Prism Formula:
A%5Btot%5D=A%5Btop%5D%2BA%5Bbot%5D%2BA%5Blat%5D

top Surface Area of a Triangular Prism Formula:

A%5Btop%5D=%281%2F4%29%2Asqrt%28%28a%2Bb%2Bc%29%28b%2Bc-a%29%28c%2Ba-b%29%28a%2Bb-c%29%29

A%5Btop%5D+=%281%2F4%29%2Asqrt%28%2817m%29%289m%29%285m%29%283m%29%29
A+%5Btop%5D=%281%2F4%29%2A47.906158m%5E2
A%5Btop%5D+=11.977m%5E2

Bottom Surface Area of a Triangular Prism Formula: This is the same area as the top surface area.
A%5Bbot%5D=11.977m%5E2
Lateral Surface Area of a Triangular Prism Formula:
A%5Blat%5D=h%28a%2Bb%2Bc%29
A%5Blat%5D=9m%284m%2B6m%2B7m%29
A%5Blat%5D=9m%2A17m
A%5Blat%5D=153m%5E2

A%5Btot%5D=11.977m%5E2%2B11.977m%5E2%2B153m%5E2
A%5Btot%5D=176.954m%5E2


Find the volume (in cubic meters) of the prism. (Round your answer to three decimal places.
Volume of a Triangular Prism Formula
Finds the 3-dimensional space occupied by a triangular prism.

V+=%281%2F4%29h%2Asqrt%28%28a%2Bb%2Bc%29%28b%2Bc-a%29%28c%2Ba-b%29%28a%2Bb-c%29%29

V+=2.25m%2Asqrt%28%2817m%29%289m%29%285m%29%283m%29%29
V+=2.25m%2Asqrt%282295m%5E4%29
V+=2.25m%2A47.906158m%5E2
V+=+107.789m%5E3

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This is intended as an addendum or supplement to MathLover1's solution.

As an alternative formula to calculate the area of a triangle, we can use Heron's Formula.

First we need to calculate the semiperimeter
s = semiperimeter
s = (perimeter)/2
s = (a+b+c)/2
s = (4+6+7)/2
s = 8.5

Then we can calculate the area
A+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29

A+=+sqrt%288.5%288.5-4%29%288.5-6%29%288.5-7%29%29

A+=+sqrt%28143.4375%29

A+=+11.9765395670034

A+=+11.977