Key takeaway: The area of a parallelogram equals its base times its perpendicular height, because cutting off a triangle and sliding it to the other side turns the shape into a rectangle.
Grade 66.G.A.1Geometry and Measurement
Definition of Area of a Parallelogram
The area of a parallelogram measures the surface enclosed by a four-sided figure whose opposite sides are parallel. The leaning sides look like a complication, yet one cut removes it.
Cut a right triangle off the left edge along a perpendicular line, carry it across, and glue it onto the right edge. The leaning figure becomes a rectangle with unchanged base and unchanged height, so nothing was gained or lost. The base is any side, and the height is the perpendicular gap between that side and the opposite one. The length of the tilted side takes no part in the calculation.
Formula and notation
Using words for the two measurements that matter:
\[A = \text{base} \times \text{height}\]
The slanted side equals the height only in a rectangle. Measure both in the same unit; the result is in square units.
Key facts
- The area of a parallelogram uses only the base and the perpendicular height.
- The height is drawn at a right angle to the base, usually as a dashed segment.
- A rectangle is a parallelogram whose height equals its slanted side.
- Two parallelograms with equal bases and equal heights cover equal surfaces.
Area of a Parallelogram example
A leaning label for a spice jar is shaped like a parallelogram. Its bottom edge is 11 cm, its slanted edge is 8 cm, and the straight-up gap between top and bottom is 6.4 cm. How much paper does it cover?
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The base is 11 cm and the height is 6.4 cm. The 8 cm side is only the slant, so it is not used.
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Multiply: \(A = 11 \times 6.4\).
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\(11 \times 6.4 = 70.4\).
The label covers 70.4 square centimeters.
Common mistake
Watch out
Ana multiplies the two side lengths and reports \(11 \times 8 = 88\) square centimeters.
Why it is wrong
The side of 8 cm is slanted, so the figure is not a rectangle. Multiplying two neighboring sides overestimates the area of a parallelogram. Use the perpendicular height: \(11 \times 6.4 = 70.4\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement