Area of Parallelograms Key Vocabulary Base of a

Area of Parallelograms

Key Vocabulary Base of a parallelogram Height of a parallelogram Parallelogram Rhombus

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 e base

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.

Area of Parallelogram What is the area of this parallelogram? b=base h=height

Area of Parallelogram What is the area of this parallelogram? b=base CUT HERE! h=height

Area of Parallelogram What is the area of this parallelogram? h=height b=base MOVE TO HERE!

Area of Parallelogram It’s the same as the area of this rectangle b=base h=height

Area of Parallelogram Arearectangle= base x height (perpendicular height h) b=base h=height

Area of Parallelogram Areaparallelogram = base x height (perpendicular height h) b=base h=height

Area of Parallelogram Words: =(base)(height) Area Symbols: A = bh h b Very Important: The height must be perpendicular to the base.

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 ANSWER square meters.

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 = 12 h Substitute 78 for A and 12 for b. 6. 5 = h Divide each side by 12. ANSWER The parallelogram has a height of 6. 5 feet.

Your Turn: Find the area of the parallelogram. 1. ANSWER 2. 3. 96 yd 2 ANSWER 77 mm 2 ANSWER 196 ft 2

Your Turn: In Exercises 4– 6, A gives the area of the parallelogram. Find the missing measure. 4. A = 72 in. 2 5. A = 30 m 2 ANSWER h = 6 in. ANSWER b=6 m ANSWER h = 4 cm 6. A = 28 cm 2

Area of a Rhombus Same as Area of parallelogram h A=b. h b