SOLUTION: This is from a worksheet. A triangular prism has a height of 12m. What is the surface area of the prism if its bases are right triangles with legs 3 meters and 4 meters? (S=Ph+2B

Algebra ->  Surface-area -> SOLUTION: This is from a worksheet. A triangular prism has a height of 12m. What is the surface area of the prism if its bases are right triangles with legs 3 meters and 4 meters? (S=Ph+2B      Log On


   

Question 163654: This is from a worksheet.
A triangular prism has a height of 12m. What is the surface area of the prism if its bases are right triangles with legs 3 meters and 4 meters? (S=Ph+2B).
I must show my work. Please help.
Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You have the formula for the surface area of the triangular prism:
S+=+Ph%2B2B where: P = perimeter of the base, h = the height of the prism, and B = the area of the base.
You are given:
h+=+12m.
You can find P from knowing the lengths of the sides of the right triangular base in which the two legs are 3m and 4m, so the hypotenuse must be 5m which you can show by using the Pythagorean theorem:
c%5E2+=+a%5E2%2Bb%5E2 c is the hypotenuse, a and b are the two legs (3m and 4m), so...
c%5E2+=+3%5E2%2B4%5E2
c%5E2+=+9%2B16
c%5E2+=+25 Take the square root of both sides.
c+=+5 Ignoring the negative solution.
The perimeter is:
P+=+3%2B4%2B5
P+=+12m
The area of the triangular base (B) is:
B+=+%281%2F2%29bh
B+=+%281%2F2%29%283%2A4%29%29
B+=+6sq.m
Now we have all we need to calculate the surface area (S) of the right-triangular prism.
S+=+Ph%2B2B Making the appropriate substitutions, we get:
S+=+12%2A12%2B2%2A6
S+=+144%2B12
P+=+156sq.m