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Area of Parallelograms, Trapezoids and Circles Help

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By — McGraw-Hill Professional
Updated on Sep 22, 2011

Area of Parallelograms, Trapezoids, and Circles

Area of a Parallelogram

The area of a parallelogram can be found by using the formula A = bh, where b is the base and h is the height or altitude .

Example 1

Find the area of the parallelogram shown in Fig. 9-12 .

SOLUTION

Fig. 9-12.

Solution 1

SOLUTION

Area of a Trapezoid

A trapezoid has a height and two bases – a lower base, b 1 , and an upper base, b 2 (see Fig. 9-13).

SOLUTION

Fig. 9-13.

The area of a trapezoid can be found by using the formula SOLUTION

Example 2

Find the area of the trapezoid shown in Fig. 9-14 .

SOLUTION

Fig. 9-14.

Solution 2

SOLUTION

Area of a Circle

The area of a circle can be found by using the formula A πr 2 , where π = 3.14 and r is the radius .

Example 3

Find the area of the circle shown in Fig. 9-15 . Use π 3.14.

SOLUTION

Fig. 9-15.

Solution 3

SOLUTION

Converting Units

The following suggestions will help you to convert between units. To change:

  • square feet to square inches, multiply by 144;
  • square inches to square feet, divide by 144;
  • square yards to square feet, multiply by 9;
  • square feet to square yards, divide by 9.

Examples

Example 4

Change 1728 square inches to square feet.

Solution 4

SOLUTION

Example 5

Change 15 square yards to square feet.

Solution 5

SOLUTION

Area of Parallelograms, Trapezoids and Circles Practice Problems

Practice

1. Find the area of a parallelogram whose base is 22 inches and whose height is 10 inches.

2. Find the area of a trapezoid whose bases are 32 feet and 44 feet and whose height is 20 feet.

3. Find the area of a circle whose radius is 14 inches. Use π = 3:14.

4. Find the area of a circle whose diameter is 32 feet. Use π = 3:14.

5. Change 12 square feet to square inches.

6. Change 27 square feet to square yards.

7. Change 2 square yards to square inches.

Answers

1. 220 in. 2

2. 760 ft 2

3. 615.44 in. 2

4. 803.84 ft 2

5. 1728 in. 2

6. 3 yd 2

7. 2592 in. 2

Practice problems for these concepts can be found at: Informal Geometry Practice Test.

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