**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 1**

**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).

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

**Example 2**

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

**Solution 2**

**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 3**

**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**

**Example 5**

Change 15 square yards to square feet.

**Solution 5**

**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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