For prisms, the fastest way to find the volume is to multiply the area of the base (whatever it is) times the height.
V = Bh
What is the volume of this prism?
Step 1: Find the area of the base. It's a triangle, so we know that the area equals half the base times the height. We only know the height.
Step 0: We know the height is 9 centimeters and the hypotenuse is 14 centimeters, but what about the base? Pythagorean theorem, here we come.
a2 + b2 = c2
(9 cm)2 + b2 = (14 cm)2
b ≈ 10.72 cm
Step 1: Find the area of the base...take two.
B = ½bh
B = ½(9 cm)(10.72 cm)
B ≈ 48.26 cm2
Step 2: Find the volume. In this case, the height is the length of the prism, not the height of the triangle.
V = Bh
V = (48.26 cm2)(12 cm)
Prepare for centimeters cubed.
V ≈ 579 cm3
Awww, yeah.To mix up things a little, here is a video on the surface area and volume of a cube: