Exercise 29 Page 627

The area of a trapezoid is one half the product of its height and the sum of its bases. Let's consider the given diagram.

In the given diagram, we can see that the length of one of the bases is b_1= 3 centimeters. To find the length of the other base we will use the Segment Addition Postulate. b_2: 4+1=5 cm

Let's use a right triangle to find the height h.

The length of the hypotenuse is 3 centimeters and the length of one of the legs is 1 centimeter. The length of the missing leg is also the height of the trapezoid. We can find it by substituting a= 1, b=h, and c=3 into the Pythagorean Theorem. Let's do it!

a^2+b^2=c^2

SubstituteValues

Substitute values

1^2+h^2=3^2

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Solve for h

CalcPow

Calculate power

1+h^2=9

SubEqn

LHS-1=RHS-1

h^2=8

SqrtEqn

sqrt(LHS)=sqrt(RHS)

h=sqrt(8)

Recall that h represents a side of a triangle and the height of the trapezoid. Therefore, we only kept the principal root when solving the equation because h must be positive. The height of the trapezoid is sqrt(8) centimeters.

Having the height and the lengths of the bases, we can substitute them into the formula for the area of a trapezoid.

A=1/2h(b_1+b_2)

SubstituteValues

Substitute values

A=1/2(sqrt(8))( 3+5)

▼

Evaluate right-hand side

AddTerms

Add terms

A=1/2(sqrt(8))(8)

UseCalc

Use a calculator

A=11.31370...

RoundDec

Round to 1 decimal place(s)

A≈ 11.3

The area of the trapezoid is approximately 11.3cm^2.