Area of a Parallelogram
In short: The area of a parallelogram is a side used as base multiplied by the straight-up height to the opposite side, A = bh, ignoring the leaning edge.
6th GradeGeometry6.G.A.1
What is Area of a Parallelogram?
Understanding the area of a parallelogram means turning it into a rectangle. Snip a right triangle from the leaning left end, slide it over to the right end, and the new shape has the same base and height.
Precisely, \(A = b h\), where \(b\) is the length of a side used as the base and \(h\) is the perpendicular distance between the two parallel bases. The slanted side is longer than the height and is not used in the formula.
How to spot it
- A shape has two pairs of parallel sides but its corners are not right angles.
- A diagram shows a dashed vertical segment drawn from the top side down to the base.
- A side length is listed that is longer than the height, tempting you to use it.
- The question asks how much material, paint or ground a slanted four-sided panel covers.
The method
- Pick a side as the base and note its length.
- Find the perpendicular height between that base and the opposite side.
- Multiply base by height, ignoring the slanted side.
- Report the area of a parallelogram in square units, and test it against the matching rectangle.
Area of a Parallelogram: solved example
Problem
A solar panel in Albuquerque is shaped like a parallelogram with a base of 8.5 feet, a leaning side of 5 feet, and a perpendicular height of 4.2 feet. How much surface does it cover?
Solution
Use the base and the perpendicular height. The slanted side of 5 feet is not needed.
\(A = 8.5 \cdot 4.2 = 35.7\). The panel covers 35.7 square feet.
Try it
Question 1
Find the area of a parallelogram with base 15 m and height 6.4 m.
Show the answer
\(15 \cdot 6.4 = 96\) square meters.
Question 2
A parallelogram has area 135 cm² and height 9 cm. What is the base?
Show the answer
\(b = 135 \div 9 = 15\) cm.
Area of a Parallelogram vs. Area of a Triangle
Cut a parallelogram along a diagonal and you get two equal triangles. So the triangle formula is half of this one, \(\frac{1}{2}bh\), and this one has no one half.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 6th Grade · Geometry