PRE-ALGEBRA

PRE-ALGEBRA

Lesson 10-1 Warm-Up

PRE-ALGEBRA

Area: Parallelograms (10-1)

area: the number of square units (squares) that the figure encloses (in other words, the number of squares that cover an area). Example: The following rectangle encloses 8 square units. If each unit is 1 cm. long on each side (1 sq. cm. or 1 cm.2), then the rectangle is 8 square cm. (or 8 cm.2).

You can find the area of a rectangle by using the formula:

area = base · height (A = bh),

where the b stands for bottom and the h stands for height. In the rectangle above, the base (bottom) is 4 cm. and the height (up-down) is 2 cm., so A = 4 cm. • 2 cm. = 8 sq. cm.

Rule: When finding area, the dimensions (sides) of the figure must be in the same units.

What is “area”?

How do you find the area of a rectangle?

PRE-ALGEBRA

Area: Parallelograms (10-1)

Example: Find the area of the banner in the picture. Step 1: Convert (change) the inches to feet or feet to inches so the dimensions will all be the same.

24 in. = • = = 2 ft.

Step 2: Find the area. A = bh Use the formula for area of a rectangle.A = 2 • 4 SubstituteA = 8 square ft.

The area of the banner is 8 square feet (8 ft.2).

Since a rectangle is a parallelogram (a four-sided figure whose opposite sides are parallel), the area of a parallelogram is the same as rectangle (A = bh). However, the height in a parallelogram is the length of an altitude. The altitude is the distance perpendicular distance from the base straight to the opposite side (top).

24 in.1

1 ft.12 in.

24 ft.12

1

1

2

1

How do you find the area of a parallelogram?

PRE-ALGEBRA

Area: Parallelograms (10-1)

Example: Find the area of each parallelogram.

The area of each parallelogram is 28 sq. in. (28 in.2).

PRE-ALGEBRA

Find the area of the rectangle.

Step 1: Convert units.

= 1.5m Multiply.

Area: ParallelogramsLESSON 10-1

Additional Examples

150 cm = 150 cm Change 150 centimeters. 1m

100cm

PRE-ALGEBRA

Step 2: Find the area.

A = bh Use the formula for area of a rectangle.

= (4)(1.5) Substitute.

= 6 Simplify.

The area of the rectangle is 6 m2.

(continued)

Area: ParallelogramsLESSON 10-1

Additional Examples

PRE-ALGEBRA

Find the area of each parallelogram.

a. b.

A = bh area formula

= (8)(2) Substitute.

= 16 Simplify.

The area is 16 m2. The area is 15 in.2.

A = bh

= (2.5)(6)

= 15

Area: ParallelogramsLESSON 10-1

Additional Examples

PRE-ALGEBRA

Find each area.

1. rectangle ABFE

2. parallelogram ACFD

3. a rectangle with a base of 50 cm and a height of 5 cm

250 cm2

40 cm2

48 cm2

Area: ParallelogramsLESSON 10-1

Lesson Quiz