Question

I need somebody to help explain this question to me: (SC will be posted below)
The volume of a right triangular prism is 72 cubic feet. The height of the prism is 9 feet. The triangular base is an isosceles right triangle.

A right triangular prism has a volume of 72 cubic feet. Triangles A E C and B F D are the base triangles. Sides F D and B F are congruent and form a right angle. The height of the prism is 9 feet.

What is the area of the triangular base?

16
square feet

What is the length of edge DF?

8
feet

Answer 1

(I left guesses)

Answer 2

What I have to go off of: The height is 9, which would be the tallest point on the triangular prism, which is BF. The image shows that BF=DF, so DF should also be 9 meaning that the area should be (9*9)/2, but it is not that

Answer 3

@snowflake0531

Answer 4

Volume is base times height, so base times 9 equals 72
So what's base?

Answer 5

CDEF is the base

Answer 6

DBF?

Answer 7

An easy way to find is to imagine... what 2-D shape stacked up together will create that prism, in this case, it's the triangle, so yes DBF

Answer 8

What I was given says that the height is 9, and since bf is the tallest point it is 9

Answer 9

right?

Answer 10

...no

Answer 11

Since you already know that base is DBF... height would be AB/CD/EF, (they're all the same length)

Answer 12

ok

Answer 13

So what's the area of the base if base times 9 is 72

Answer 14

plugging 9*x=72 in my graphing calculator says 8

Answer 15

damn, you used a calculator

but yes, it's 8

So now \[\frac{x^2}{2}=8\\x^2=16\]
so what's the x

Answer 16

solve the square root of 16 to get 4, x would then be 4

Answer 17

yes

Answer 18

so do you get your answers now?

Answer 19

yep, thanks

Answer 20

yw~