11-4 11-4 Area of ParallelogramsArea of Parallelograms

Pages 483-485Pages 483-485

Indicator (s): P8Indicator (s): P8 Use formulas Use formulas in problem-solving situationsin problem-solving situations

Area of a ParallelogramArea of a Parallelogram

The area of a The area of a polygonpolygon is the number is the number of square units inside the polygon. of square units inside the polygon.

Area is 2-dimensional like a carpet or Area is 2-dimensional like a carpet or an area rug. an area rug.

A parallelogram is a 4-sided shape A parallelogram is a 4-sided shape formed by two pairs of formed by two pairs of parallelparallel lines. lines.

Opposite sides are equal in length Opposite sides are equal in length and opposite angles are equal in and opposite angles are equal in measure. measure.

To find the area of a parallelogram, To find the area of a parallelogram, multiply the base by the height. multiply the base by the height.

The formula is: The formula is: a=ba=b•h•h  – bb is the base is the base– hh is the heightis the height– •• means multiply. means multiply.

The base and height of a parallelogram The base and height of a parallelogram must be must be perpendicularperpendicular. However, the . However, the lateral sides of a parallelogram are not lateral sides of a parallelogram are not perpendicular to the base. Thus, a dotted perpendicular to the base. Thus, a dotted line is drawn to represent the height. line is drawn to represent the height. Let's look at some examples involving the Let's look at some examples involving the area of a parallelogram. area of a parallelogram.

Example 1Example 1

Find the area of a parallelogram with Find the area of a parallelogram with a base of 12 centimeters and a a base of 12 centimeters and a height of 5 centimeters. height of 5 centimeters.

a=ba=b•h•h aa=(12 cm)=(12 cm)··(5 cm)(5 cm)

aa= 60 cm2 = 60 cm2

Example 2Example 2 The area of a parallelogram is 24 The area of a parallelogram is 24

square centimeters and the base is 4 square centimeters and the base is 4 centimeters. Find the height. centimeters. Find the height.

a=ba=b•h•h

24cm24cm22 =(4cm) =(4cm)··hh

6cm = 6cm = hh4

)4(

4

24 2 hcmcm

Just be sure to… Just be sure to…

……multiply the multiply the basebase of the of the parallelogram times the parallelogram times the heightheight of the of the parallelogram.parallelogram.

NOTNOT base times side. base times side.

basebaseh

eig

hh

eig

htt heig

hh

eig

htt

side

side