Exercise 5 Page 840

The given solid is a prism.

To calculate the lateral area of a prism, we can use the known formula where P is the perimeter of the base and h is the height. L=Ph We are given two lengths of the base's sides, a= 7 and b= 8. The base of a given prism is a right triangle, so we can use The Pythagorean Theorem in order to calculate the missing length.

a^2+b^2=c^2

SubstituteII

a= 7, b= 8

7^2+ 8^2=c^2

▼

Simplify

CalcPow

Calculate power

49+64=c^2

RearrangeEqn

Rearrange equation

c^2=49+64

AddTerms

Add terms

c^2=113

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=sqrt(113)

Now, let's add these three side lengths to find the perimeter of the base. P&=7+8+sqrt(113) P&=15+sqrt(113)cm Now we have enough information to find the lateral area of the prism. Let's substitute 15+sqrt(113) and 10 for P and h, respectively.

L=Ph

SubstituteII

P= 15+sqrt(113), h= 10

L=( 15+sqrt(113))( 10)

Distr

Distribute 10

L=150+10sqrt(113)

UseCalc

Use a calculator

L=256.301458...

RoundDec

Round to 1 decimal place(s)

L≈ 256.3

The lateral area of the prism is 256.3cm^2.