Exercise 16 Page 818

We are asked to find the lateral area and surface area of a triangular prism. Let's do these things one at a time.

Lateral area

We will recall the formula for the lateral area L of a prism. L=Ph Here, P is the perimeter of the base, and h the height of the prism. Note that the base is a right triangle. We know that the lengths of the legs of this triangle are 12in and 9in. We can find the hypotenuse by using the Pythagorean Theorem.

c^2 = a^2 + b^2

SubstituteII

a= 12, b= 9

c^2= 12^2 + 9^2

▼

Solve for c

CalcPow

Calculate power

c^2 = 144 + 81

AddTerms

Add terms

c^2 = 225

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c= 15

Now we know the lengths of the three sides of the base. Let's add them to find its perimeter. P&= 15+ 12+ 9 P&= 36in Let's now substitute P= 36 and h= 6 in the formula for the lateral area of a prism.

L=Ph

SubstituteII

P= 36, h= 6

L= 36( 6)

Multiply

Multiply

L=216

The lateral area of the solid is 216 in^2. Note that the lateral area may change if we were to consider another dimension as the base.

Surface Area

Let's recall the formula for the surface area of a prism. S=L+2B Here, L is the lateral area of the prism and B the area of the base. We already know that L=216in^2. We can calculate the area of the base using the formula for area of a triangle.

B=1/2bh

SubstituteII

h= 12, b= 9

B=1/2( 9)( 12)

▼

Evaluate right-hand side

MoveRightFacToNumOne

1/b* a = a/b

B=108/2

CalcQuot

Calculate quotient

B=54

The area of the base is 54in^2. Now we have enough information to find the surface area of the prism. Let's substitute 216 and 54 for L and B, respectively, into the corresponding formula.

S=L+2B

SubstituteII

L= 216, B= 54

S=216+2(54)

▼

Evaluate right-hand side

Multiply

Multiply

S=216+108

AddTerms

Add terms

S=324

The surface area of the prism is 324in^2.