ESSENTIAL QUESTION: How do you find the area of parallelograms? 8.5 ESSENTIAL QUESTION: How do you find the area of parallelograms?

VOCABULARY Either pair of parallel sides of a parallelogram are called the bases of the parallelogram.

VOCABULARY Either pair of parallel sides of a parallelogram are called the bases of the parallelogram. The shortest distance between the bases of a parallelogram is called the height of a parallelogram.

Area of a Parallelogram

Find the area of the parallelogram. Example 1 Find the Area of a Parallelogram Find the area of the parallelogram. SOLUTION Use the formula for the area of a parallelogram. Substitute 9 for b and 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. ANSWER

Find the height of the parallelogram Example 2 Find the Height of a Parallelogram Find the height of the parallelogram given 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

Find the area of the parallelogram. Checkpoint Area of Parallelograms Find the area of the parallelogram. 1. 2. 3. ANSWER 77 mm2 ANSWER 96 yd2 ANSWER 196 ft2

Find the area of the parallelogram. Checkpoint Area of Parallelograms Find the area of the parallelogram. 1. ANSWER 96 yd2 2. ANSWER 77 mm2 3. ANSWER 196 ft2 9

Checkpoint Area of Parallelograms In Exercises 4–6, A gives the area of the parallelogram. Find the missing measure. 4. A = 72 in.2 5. A = 30 m2 6. A = 28 cm2

Checkpoint Area of Parallelograms In Exercises 4–6, A gives the area of the parallelogram. Find the missing measure. 4. A = 72 in.2 ANSWER h = 6 in. 5. A = 30 m2 ANSWER b = 6 m 6. A = 28 cm2 ANSWER h = 4 cm 11

Area of a Rhombus

Find the area of the rhombus. Example 3 Find the Area of a Rhombus Find the area of the rhombus. a. b. SOLUTION b. A = d1d2 2 1 SOLUTION A = d1d2 2 1 a. (6 + 6)(9 + 9) = 2 1 2 1 (14)(10) = (12)(18) = 2 1 = 70 = 108 The area of the rhombus is 70 square inches. The area of the rhombus is 108 square inches. 15

Find the area of the triangle. 1. ANSWER 49 in.2 2. ANSWER 168 m2

In Exercises 3 and 4, A gives the area of the triangle In Exercises 3 and 4, A gives the area of the triangle. Find the missing measure. 3. A = 65 ft2 ANSWER h = 10 ft 4. A = 27 cm2 ANSWER b = 9 cm A triangular sail of a boat has a base 5 feet long and the sail has an area of 20 square feet. What is the height of the sail? 5. ANSWER 8 ft

Worksheet 8.5A