Area of Parallelograms Section 8.5

Goal Find the area of parallelograms.

Key Vocabulary Base of a parallelogram Height of a 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 base base 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? h=height b=base

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

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

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

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

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

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

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

Your Turn: Find the area of the parallelogram. 1. ANSWER 96 yd2 2. ANSWER 77 mm2 3. ANSWER 196 ft2

Your Turn: 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