Area of Parallelograms

1 / 22

# Area of Parallelograms - PowerPoint PPT Presentation

Area of Parallelograms. Section 11.2. Goal. Find the area of parallelograms. Key Vocabulary. Base of a parallelogram Height of a parallelogram Parallelogram Rhombus . Parallelogram. A parallelogram is a quadrilateral where the opposite sides are congruent and parallel.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Area of Parallelograms

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Area of Parallelograms

Section 11.2

Goal
• Find the area of parallelograms.
Key Vocabulary
• Base of a parallelogram
• Height of a parallelogram
• Parallelogram
• Rhombus
Parallelogram
• A parallelogram is a quadrilateral where the opposite sides are congruent and parallel.
• A rectangle is a type of parallelogram, but we often see parallelograms that are not rectangles (parallelograms without right angles).
The Base of a Parallelogram
• Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.

base

base

base

base

The Height of a Parallelogram
• The shortest distance (perpendicular distance) between the bases of a parallelogram is called the height of the parallelogram.
• The height of the parallelogram is always perpendicular to the bases.
Area of Parallelogram

What is the area

of this parallelogram?

h=height

b=base

Area of Parallelogram

What is the area

of this parallelogram?

h=height

b=base

CUT HERE!

Area of Parallelogram

What is the area

of this parallelogram?

h=height

b=base

MOVE TO HERE!

Area of Parallelogram

It’s the same as

the area of this rectangle

h=height

b=base

Area of Parallelogram

Arearectangle= base x height

(perpendicular height h)

h=height

b=base

Area of Parallelogram

Areaparallelogram = base x height

(perpendicular height h)

h=height

b=base

Area of Parallelogram
• Words: Area =(base)(height)
• Symbols: A = bh

h

b

Very Important: The height must be perpendicular to the base.

SOLUTION

Use the formula for the area of a parallelogram.

Substitute 9 for band 6 for h.

A = bh

Formula for the area of a parallelogram

=(9)(6)

Substitute 9 for b and 6 for h.

=54

Multiply.

The parallelogram has an area of 54

square meters.

Example 1

Find the Area of a Parallelogram

Find the area of the parallelogram.

A =bh

Formula for the area of a parallelogram

78=12h

Substitute 78 for A and 12 for b.

6.5 =h

Divide each side by 12.

The parallelogram has a height of 6.5 feet.

Example 2

Find the Height of a Parallelogram

Find the height of the parallelogram

given that its area is 78 square feet.

SOLUTION

1.

96 yd2

2.

77 mm2

3.

196 ft2

Find the area of the parallelogram.

4.

A = 72 in.2

h =6 in.

A = 30 m2

5.

b =6 m

6.

A = 28 cm2

h =4 cm

In Exercises 4–6, Agives the area of the parallelogram. Find the missing measure.

Rhombus
• A parallelogram with opposite equal acute and obtuse angles and four equal sides.

Diagonals

4 equal sides

Diagonals

h

b

Area of a Rhombus

Same as Area of parallelogram

A = b . h

d2

d1

Special “Rhombus Rule”
• Since the diagonals are perpendicular
• Another way to find the area of a rhombus is:
• Area = ½ (product of the diagonals)

area = ½ (d1.d2)

This is good when you only know the diagonals, but not the sides or height

Area of a Rhombus

The formula for the area of a rhombus can be justified using the area of a triangle. A specific case follows.

• The diagonals divide a rhombus into 4 congruent right triangles. So, the area of the rhombus is 4 times the area of one of the right triangles.
• Area of 1 triangle = 1/2bh = ½(3)(4) = 6
• Area of 4 triangles = 4(6) = 24
• Notice that 1/2d1d2 or ½(6)(8), also equals 24

Find the area of the rhombus.

b.

a.

1

1

1

1

1

2

2

2

2

2

Example 3

Find the Area of a Rhombus

SOLUTION

SOLUTION

a.

b.

A=d1d2

A=d1d2

=

(6 + 6)(9 + 9)

=

(14)(10)

= 70

=

(12)(18)

=108

The area of the rhombus is 70 square inches.

The area of the rhombus

is 108 square inches.