Parallelogram area

Area of parallelogram and examples

1. Area of Parallelograms

2. Goal Find the area of parallelograms.

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

4. 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).

5. The Base of a Parallelogram Either pair of parallel sides of a parallelogram are called the bases of the parallelogram . base base base base

6. 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.

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

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

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

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

11. Area rectangle = base x height (perpendicular height h) h=height b=base Area of Parallelogram

12. Area parallelogram = base x height (perpendicular height h) b=base h=height Area of Parallelogram

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

14. Find the Area of a Parallelogram Example 1 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 = b h 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

15. Find the Height of a Parallelogram Example 2 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 . The parallelogram has a height of 6.5 feet. ANSWER

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

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

18. Rhombus A parallelogram with opposite equal acute and obtuse angles and four equal sides. Diagonals Diagonals 4 equal sides

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