Parallelograms
The area of a parallelogram is calculated as A = base × height, where the height is the perpendicular (vertical) distance between the parallel bases, not the slanted side length. In Grade 6 Saxon Math Course 1, students must identify the correct height: if a parallelogram has base 10 m and perpendicular height 4 m (with a slanted side of 5 m), its area is 10 × 4 = 40 m², not 10 × 5 = 50 m². This formula is derived by rearranging a parallelogram into a rectangle of the same base and height.
Key Concepts
New Concept A parallelogram is a quadrilateral with two pairs of parallel sides. Its area is found by multiplying the base by the height, as shown in the formula:.
$$A = bh$$ What’s next This is just the foundation. Next, you'll walk through worked examples to calculate the area, perimeter, and unknown angles of different parallelograms.
Common Questions
What is the formula for the area of a parallelogram?
A = base × height, where height is the perpendicular distance between the parallel sides.
A parallelogram has base 10 m, slanted side 5 m, and perpendicular height 4 m. What is its area?
A = 10 × 4 = 40 m². The slanted side is not the height.
Why do you use perpendicular height, not the slanted side?
Area measures the flat space enclosed. The perpendicular height gives the true vertical extent of the figure; the slanted side does not.
How is a parallelogram's area related to a rectangle's area?
You can cut a triangle from one end of a parallelogram and reattach it to the other to form a rectangle with the same base and height — and thus the same area.
What is the area of a parallelogram with base 8 cm and height 6 cm?
A = 8 × 6 = 48 cm².