Exercise 31 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 diagram we can see that the lengths of the bases are b_1= 0.9 meters and b_1=2.1 meters. Let's indicate the height, h, in the diagram.

To find the length of the triangle's opposite side — which is also the height of the trapezoid — we will use the sine ratio . sin θ = Opposite/Hypotenuse If we let h be the length of the opposite side of the triangle, we can substitute the corresponding values in the above equation to find its length.

sin θ = Opposite/Hypotenuse

SubstituteValues

Substitute values

sin 45^(∘) = h/1.7

▼

Solve for h

MultEqn

LHS * 1.7=RHS* 1.7

sin 45^(∘) * 1.7= h

UseCalc

Use a calculator

1.20208...=h

RearrangeEqn

Rearrange equation

h=1.20208...

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(1.20208...)( 0.9+2.1)

▼

Evaluate right-hand side

AddTerms

Add terms

A=1/2(1.20208...)(3)

UseCalc

Use a calculator

A=1.80312...

RoundDec

Round to 1 decimal place(s)

A≈ 1.8

The area of the trapezoid to the nearest tenth is 1.8m^2