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Area of Parallelograms
GoalFind the area of parallelograms.
Key VocabularyBase of a parallelogramHeight of a parallelogramParallelogramRhombus
ParallelogramA 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
baseba
se
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.
What is the area of this parallelogram?
b=base
h=height
Area of Parallelogram
What is the area of this parallelogram?
CUT HERE!
b=base
h=height
Area of Parallelogram
What is the area of this parallelogram?
MOVE TO HERE!
b=base
h=height
Area of Parallelogram
It’s the same as the area of this rectangle h=height
b=base
Area of Parallelogram
Arearectangle= base x height(perpendicular height h)
h=height
b=base
Area of Parallelogram
Areaparallelogram = base x height(perpendicular height h)
b=base
h=height
Area of Parallelogram
b
h
Area of ParallelogramWords: Area =(base)(height)
Symbols: A = bh
Very Important: The height must be perpendicular to the base.
Find the Area of a ParallelogramExample 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 = 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 a ParallelogramExample 2
Find the height of the parallelogramgiven 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.
3.
2.
1.ANSWER 96 yd2
ANSWER 77 mm2
ANSWER 196 ft2
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 m2
6. A = 28 cm2
Rhombus A parallelogram with opposite equal acute and obtuse angles and four equal sides.
Diagonals
Diagonals
4 equal sides
Area of a Rhombus
Same as Area of parallelogram
A = b . h
b
h