Formula for the Area of a Parallelogram
The formula for the area of a parallelogram is a Grade 6 geometry skill in Reveal Math, Course 1. The area of a parallelogram equals base times height: A = b x h, where h is the perpendicular height, not the slant side. This formula is derived visually: cutting a right triangle from one end and reattaching it to the other transforms the parallelogram into a rectangle with the same base and height. Because the rearranged rectangle has area = l x w = base x height, the same formula applies to the parallelogram. This conceptual understanding prevents the common mistake of using the slant side as the height.
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?
A = b x h, where b is the base and h is the perpendicular height (the distance between the base and the opposite side, measured at a right angle). The slant side length is not used.
Why is the parallelogram area formula the same as a rectangle?
A parallelogram can be cut and rearranged into a rectangle with the same base and height. Since both shapes contain identical area, A = base x height works for both.
How is the height of a parallelogram different from its side length?
The height is the perpendicular distance between the two parallel bases. The slant sides are the actual sides connecting the bases, which are always longer than the perpendicular height unless the angles are 90 degrees.
Can any side of a parallelogram be the base?
Yes, any side can serve as the base. The corresponding height must then be the perpendicular distance from that base to the opposite side. Different base choices give different h values, but the product b x h always equals the same area.
What are common mistakes with the parallelogram area formula?
Using the slant side instead of the perpendicular height is the most common error. Always identify the right-angle symbol or the explicitly labeled height before substituting.
When do students learn the parallelogram area formula?
The parallelogram area formula is introduced in Grade 6 in Reveal Math, Course 1, in the area of polygons chapter.
Which textbook covers the parallelogram area formula?
Reveal Math, Course 1, used in Grade 6, covers A = b x h for parallelograms in the area chapter.