Exercise 10 Page 721

Use the formulas for area of a triangle and volume of a prism.

280.6cm^3

Practice makes perfect

We are given the following triangular prism and we want to find its volume.

Looking at our triangular prism, we can see that the base is an equilateral triangle. We know that altitude h' of the triangle divides it into two 30°- 60°- 90° triangles, where the height of the triangle is given by h'=sqrt(3)*shorter leg

As we can see in previous figure the length of the shorter leg is equal to 3cm. Therefore, we can calculate the height of the triangle. h'=sqrt(3)*shorter leg ⇔ h'=sqrt(3)* 3 Once we have the altitude h'=3sqrt(3)cm and the base b=6cm, we will find the area of the base using the formula for area of a triangle.

B=1/2bh'

SubstituteII

b= 6, h= 3sqrt(3)

B=1/2( 6)( 3sqrt(3))

▼

Simplify right-hand side

Multiply

B=1/2(18sqrt(3))

MoveRightFacToNumOne

1/b* a = a/b

B=18sqrt(3)/2

MovePartNumRight

a* b/c=a/c* b

B=18/2* sqrt(3)

CalcQuot

Calculate quotient

B=9sqrt(3)

Now the volume of a prism can be calculated using the following formula. V=Bh Since we know that the area of the base is B=9sqrt(3)cm^2 and the height is h=18cm. Let's substitute these values into the formula and solve for V.

V=Bh

SubstituteII

B= 9sqrt(3), h= 18

V=( 9sqrt(3))( 18)

UseCalc

Use a calculator

V=280.592230...

RoundDec

Round to 1 decimal place(s)

V≈280.6

Therefore, the volume of the triangular prism is 280.6cm^3.