Area of a Parallelogram
Learn to calculate the area of a parallelogram using the formula A = bh by multiplying the base times the perpendicular height in Grade 6 geometry.
Key Concepts
Property To find the area of a parallelogram, we multiply the base by the height. The formula is $A = bh$, where $b$ is the length of one side (the base) and $h$ is the perpendicular distance to the opposite side (the height).
Examples A parallelogram with a base of 10 cm and a height of 5 cm has an area of $10 \times 5 = 50$ sq. cm. A parallelogram has a base of 8 inches and a height of 4 inches, so its area is $8 \text{ in} \times 4 \text{ in} = 32$ sq. in. If a parallelogram's area is 48 sq. meters and its base is 12 meters, the height is $48 \div 12 = 4$ meters.
Explanation Finding a parallelogram's area seems tricky, but it's a magic trick! Just snip a triangle off one end, slide it to the other, and voilà—you’ve made a rectangle. Since you only moved a piece, the area is exactly the same! Now, just multiply the base by the height, which were the length and width of your new rectangle.
Common Questions
What is the formula for the area of a parallelogram?
The formula for the area of a parallelogram is A = bh, where b is the length of the base and h is the perpendicular height to the opposite side. For example, a parallelogram with a base of 10 cm and a height of 5 cm has an area of 50 square centimeters.
Why do you use the height and not the slanted side when finding the area of a parallelogram?
You use the perpendicular height because the area measures the true space inside the shape, not the length of the slanted side. Think of a parallelogram as a slanted rectangle — if you snip a triangle off one end and slide it to the other, you form a rectangle with the same base and height, proving the formula A = bh works.
How do you find the height of a parallelogram if you know the area and base?
If you know the area and the base, divide the area by the base to find the height. For example, if a parallelogram has an area of 48 square meters and a base of 12 meters, the height is 48 ÷ 12 = 4 meters.
What grade level learns the area of a parallelogram in Saxon Math?
The area of a parallelogram is taught in Grade 6 as part of Chapter 8: Advanced Topics in Geometry and Number Operations in Saxon Math, Course 1. Students learn to apply the formula A = bh to solve real problems involving parallelograms.