Area of Parallelograms

Re-cap...

What is the formula for area of rectangle?What is the formula for the surface are of a rectangle?What is the formula for the volume of a rectangular prism?

Goal

Find the area of parallelograms.

Key Vocabulary

Base of a parallelogramHeight of a parallelogramParallelogramRhombus

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

baseba

se

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.

What is the area of this parallelogram?

b=base

h=height

Area of Parallelogram

What is the area of this parallelogram?

CUT HERE!

b=base

h=height

Area of Parallelogram

What is the area of this parallelogram?

MOVE TO HERE!

b=base

h=height

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

b

h

Area of Parallelogram

Words: Area =(base)(height)

Symbols: A = bh

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

Areaparallelogram = base x height(perpendicular height h)

b=base

h=height

Area of Parallelogram

Find the Area of a RhombusExample 3

Find the area of the rhombus.

a. b.

= 108

The area of the rhombus is 70 square inches.

The area of the rhombus is 108 square inches.

SOLUTION

A = d1d221a.

SOLUTION

b. A = d1d221

21 (14)(10)= (6 + 6)(9 + 9)= 2

1

= 70 (12)(18)= 21

12.5cm

9.2 cm

Practice…

• Words: Area =(base)(height)

• Symbols: A = bh

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

Practice...

Find the Height of a ParallelogramExample 2

Find the height of the parallelogramgiven that its area is 78 square feet.

SOLUTION

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.ANSWER

Practice...Find the height

Area= 16m2

4cm

Practice...

12cm

? cm

Area= 60cm

Wrap up...

• What’s the formula for area of a parallelogram?

• How would you find the height of a parallelogram when given the area and base?