Formula for the Area of a Parallelogram
The area of a parallelogram equals base times height, written as A = bh, where b is any parallel side and h is the perpendicular distance between the two parallel sides. A parallelogram with base 12 cm and height 5 cm has area 60 square cm. The answer must always be expressed in square units. This formula, from Reveal Math, Course 1, Module 8, is derived by rearranging a parallelogram into a rectangle, proving that it takes up the same amount of space as a rectangle with the same dimensions.
Key Concepts
Property Because a parallelogram can be rearranged into a rectangle, we find its area by multiplying the base (length) by the perpendicular height. The area is given by the formula: $$A = bh$$ Always express your final answer in square units (like square cm or in²).
Session 4. Formula for the Area of a Parallelogram.
Property Because a parallelogram can be rearranged into a rectangle, we find Examples A parallelogram has a base of 12 cm and a height of 5 cm. Its area is 12 x 5 = 60 square cm. A section of a patio is shaped like a parallelogram with a base of 8 feet and a height of 6 feet. The area is 8 x 6 = 48 square feet. Spot the error: If a base is 5 m and height is 4 m, writing the area as "20 m" is incorrect. It must be "20 square meters" because area measures 2D space.
Common Questions
What is the formula for the area of a parallelogram?
The formula is A = b times h, where b is the base (any parallel side) and h is the perpendicular height between the two parallel sides. Always express the answer in square units.
How is the parallelogram area formula derived?
If you cut a right triangle from one slanted end of a parallelogram and move it to the other end, the shape becomes a rectangle with the same base and height. This proves A = bh for both shapes.
What are square units and why do we use them for area?
Square units (like cm squared or ft squared) measure 2D space. Area tells how many unit squares cover a surface, so the answer must carry a square unit, never just a linear unit.
What is the difference between base and height of a parallelogram?
The base is any of the parallel sides. The height is the perpendicular distance between those parallel sides, forming a 90-degree angle with the base. Never use the slanted side as the height.
How do I find the area of a parallelogram with base 8 ft and height 6 ft?
A = 8 times 6 = 48 square feet.
When do 6th graders learn the parallelogram area formula?
Module 8 of Reveal Math, Course 1 covers this as part of the area unit.