Exercise 13 Page 334

Before we try to find the area of the given figure, notice that the figure can be divided into a rectangle, a triangle and a parallelogram. When breaking up the figure, remember to find all the missing dimensions.

In the diagram, we can see that the length and width of the rectangle are 2 and 8 millimeters, respectively. We can also see that 8 millimeters is the base of the triangle and 5 millimeters is the height. We can also see that 8 millimeters is the base of the parallelogram. Height of the parallelogram is the missing dimension. We can use the segment addition postulate to find it. Let's do it! ccc 16= 5+ 2+ h 16- 5- 2= h 9= h

Now we have all the informations to calculate the area of each figure. Let's see the figures separately with all their dimensions labeled!

To find the area of the rectangle, we will substitute l= 2 and w= 8 into the formula for the area of a rectangle.

A=l w

SubstituteII

l= 2, w= 8

A= 2( 8)

Multiply

Multiply

A=16

The area of the rectangle is 16 square millimeters. To find the area of the triangle, we will substitute b= 8 and h= 5 into the formula for the area of a triangle, and simplify.

A=1/2bh

SubstituteII

b= 8, h= 5

A=1/2( 8)( 5)

Multiply

Multiply

A=1/2(40)

MoveRightFacToNumOne

1/b* a = a/b

A=40/2

UseCalc

Use a calculator

A=20

The area of the triangle is 20 square millimeters. To find the area of the parallelogram, we will substitute b= 8 and h= 9 into the formula for the area of a parallelogram, and simplify.

A=b* h

SubstituteII

b= 8, h= 9

A= 8( 9)

Multiply

Multiply

A=72

The area of the parallelogram is 72 square millimeters. We now know the areas of all the rectangle, the triangle and the parallelogram.

To find the total area of the figure, we add these two values. Area of the Figure 20+16+72=108mm^2 The total area of the figure is 108 square millimeters.