Exercise 52 Page 229

Examining the diagram, we see that the figure consists of a triangle and a rectangle put together. To calculate the area and perimeter we will add some information to the diagram.

Knowing a leg and one of the non-right angles in the right triangle, we can calculate the length of the unknown leg and hypotenuse, which we will label x and y, respectively. We need both of these to calculate the shape's area and perimeter.

Let's solve the equations one at a time.

tan 20^(∘) =x/6

▼

Solve for x

MultEqn

LHS * 6=RHS* 6

6tan 20^(∘) = x

RearrangeEqn

Rearrange equation

x=6tan 20^(∘)

UseCalc

Use a calculator

x=2.18382...

RoundDec

Round to 1 decimal place(s)

x≈ 2.2

Let's also solve for y, the hypotenuse.

cos 20^(∘) =6/y

▼

Solve for y

MultEqn

LHS * y=RHS* y

ycos 20^(∘) = 6

DivEqn

.LHS /cos 20^(∘).=.RHS /cos 20^(∘).

y = 6/cos 20^(∘)

UseCalc

Use a calculator

y=6.38506...

RoundDec

Round to 1 decimal place(s)

y≈ 6.4

With this information we can determine the figure's unknown sides and perimeter.

To determine the area we will calculate the area of the triangle and rectangle separately and then add them.