Area of a parallelogram
The area of a parallelogram is calculated with the formula A = bh, where b is the base and h is the perpendicular height (not the slant side). The height must form a right angle with the base. This formula works because a parallelogram has the same area as a rectangle with the same base and height — you can imagine cutting a triangle off one end and reattaching it to the other to form a rectangle. For example, a parallelogram with base 8 cm and height 5 cm has area 8 × 5 = 40 cm². This is covered in Saxon Math, Course 2, as part of 7th grade geometry.
Key Concepts
Property Area of a parallelogram = base · height $$A = bh$$.
Examples A park with a base of 80 yards and a height of 40 yards has an area of $80 \times 40 = 3200$ square yards. A piece of paper with a base of 10 cm and a height of 9 cm has an area of $10 \times 9 = 90$ square cm.
Explanation Imagine you snip a triangle off one side and slide it to the other. Presto! You've magically transformed the parallelogram into a rectangle. That's why the area is simply its base multiplied by its straight up height, not the slanted side length.
Common Questions
What is the formula for the area of a parallelogram?
A = bh, where b is the base and h is the perpendicular height (the height at a right angle to the base, not the slant side).
What is a parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. Rectangles, rhombuses, and squares are all special types of parallelograms.
Why is the area of a parallelogram equal to base times height?
A parallelogram can be rearranged into a rectangle with the same base and height by cutting a triangular piece from one end and moving it to the other. Since the rectangle’s area is lw = bh, the parallelogram has the same area.
What is the difference between height and slant height in a parallelogram?
The height (used in the formula) is the perpendicular distance between the two bases — it forms a right angle. The slant height is the length of the slanted side, which is longer and should NOT be used in the area formula.
What is the area of a parallelogram with base 10 and height 6?
A = bh = 10 × 6 = 60 square units.
When do students learn about the area of a parallelogram?
The area of a parallelogram is typically introduced in 6th grade and extended with more complex applications in 7th grade geometry.
Which textbook covers the area of a parallelogram?
Saxon Math, Course 2 covers the area of a parallelogram using the formula A = bh.