Exercise 22 Page 784

The area of a parallelogram is the product of a base and its corresponding height.

We can consider the side whose length is 22cm as the base. However, we need to find the height. To do so, we will pay close attention to the right triangle formed at the bottom of the diagram.

We know the length of one of the legs of this triangle, and we want to find the length of the other leg h. We are also given the measure of the angle that is opposite the leg which measures 18 cm. To find h, we can use the tangent ratio. tan 40 ^(∘) = 18/h Let's find h by solving the above equation.

tan 40^(∘)=18/h

▼

Solve for h

MultEqn

LHS * h=RHS* h

h tan 40^(∘)=18

DivEqn

.LHS /tan 40 ^(∘).=.RHS /tan 40 ^(∘).

h = 18/tan 40 ^(∘)

UseCalc

Use a calculator

h=21.451564...

RoundDec

Round to 4 decimal place(s)

h ≈ 21.4516

Therefore, the height of the parallelogram is approximately 21.4516cm. Note that we round the length of the height to four decimal places so that the final answer is more exact.

Now that we know that the base is 22cm and that the height is 21.4516cm, we can substitute these values in the formula for the area of a parallelogram.

A=bh

SubstituteII

b= 22, h= 21.4516

A=(22)(21.4516)

▼

Evaluate right-hand side

Multiply

Multiply

A=471.9352

RoundDec

Round to 1 decimal place(s)

A ≈ 471.9

The area of the parallelogram to the nearest tenth is 471.9 square centimeters.