Finding a Missing Dimension
When the area of a parallelogram and one dimension are known, the missing dimension can be found by treating A = bh as an algebra equation and dividing. If area = 60 sq cm and base = 12 cm, solve 60 = 12h by dividing both sides by 12, giving h = 5 cm. If area = 48 sq ft and height = 6 ft, the base = 48 divided by 6 = 8 ft. This reverse-formula skill, from Reveal Math, Course 1, Module 8, shows 6th grade students that area formulas can be used both forward and backward.
Key Concepts
Property When you know the area of a parallelogram and one dimension (either the base or the height), you can use the area formula $$A = bh$$ like an algebra equation and divide to find the missing piece.
Examples A parallelogram has an area of 60 square cm and a base of 12 cm. To find the height, set up the equation 60 = 12h. Divide 60 by 12 to get h = 5 cm. A parallelogram shaped garden has an area of 48 square feet and a height of 6 feet. To find the base, set up 48 = b x 6. Divide 48 by 6 to get b = 8 feet.
Explanation Formulas work in both directions! If you know the two pieces that make the area, you multiply. If you know the total area and want to work backward to find a missing piece, you simply do the opposite of multiplication: division.
Common Questions
How do I find a missing dimension of a parallelogram from its area?
Divide the area by the known dimension. If A = bh and you know A and b, then h = A divided by b. If you know A and h, then b = A divided by h.
A parallelogram has area 72 sq in and height 8 in. What is the base?
Base = 72 divided by 8 = 9 inches.
A parallelogram has area 45 sq m and base 9 m. What is the height?
Height = 45 divided by 9 = 5 meters.
Why does dividing by one dimension give you the other?
The area formula A = bh is a multiplication equation. Division is the inverse of multiplication, so dividing both sides by the known dimension isolates the missing one.
Can I use this method if I have fractional or decimal dimensions?
Yes. The same method applies: area divided by known dimension equals missing dimension, regardless of whether the numbers are whole numbers, fractions, or decimals.
When do 6th graders learn to find missing parallelogram dimensions?
Module 8 of Reveal Math, Course 1 covers this as an extension of the parallelogram area formula.