Exercise 57 Page 60

We are told that the area A of the given trapezoid is less than 18 square centimeters. A < 18cm^2 Recall the formula for the area of a trapezoid. A=1/2(a+b)h In the above formula, a is the longer base, b is the shorter base, and h is the height. Let's substitute this expression for A in our inequality. 1/2(a+b)h< 18 We are also given the height of the trapezoid, h= x, and the bases, a= 8 and b= 4. If we substitute these values into our inequality, we will be able to solve for x.

1/2(a+b)h<18

SubstituteIII

Substitute a= 8,b= 4,h= x

1/2( 8+ 4) x<18

▼

Simplify left-hand side

AddTerms

Add terms

1/2(12)x<18

MoveRightFacToNumOne

1/b* a = a/b

12/2x<18

CalcQuot

Calculate quotient

6x<18

DivIneq

.LHS /6.<.RHS /6.

x<3

This inequality tells us that, for the area of a trapezoid with bases 8cm and 4cm to be less than 18cm^2, the height must be less than 3cm. x< 3cm