Area of Parallelograms Formula

Area of parallelograms are the area of a parallelogram is the product of its base and perpendicular height: A = bh.

The Formula

A=bhA = bh

When to use: Cut a triangle off one end of the parallelogram and slide it to the other end — you get a rectangle with the same base and height.

Quick Example

A parallelogram with base 8 cm and height 5 cm has area 8×5=408 \times 5 = 40 cm2^2.

Notation

bb = base, hh = perpendicular height

What This Formula Means

The area of a parallelogram is the product of its base and perpendicular height: A=bhA = bh.

Cut a triangle off one end of the parallelogram and slide it to the other end — you get a rectangle with the same base and height.

Worked Examples

Example 1

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A parallelogram has base 1414 and height 55. If both are doubled, find the new area.

Answer

280

First step

1
Original area =14×5=70=14\times 5=70.

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Example 2

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A parallelogram has sides 88 and 1010 with included angle 60°60°. Find its area.

Example 3

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A parallelogram-shaped tile has base 2020 cm and slant side 1313 cm. The height to the base is 1212 cm. Find the tile's area.

Common Mistakes

  • Using the slanted side as the height - the height is the perpendicular distance between the two parallel bases.
  • Halving the product like a triangle - a parallelogram uses the full bhbh, no 12\frac{1}{2}.
  • Reporting the answer in linear units - area is in square units (cm², in²).

Why This Formula Matters

It is the hinge between rectangle area and the triangle and trapezoid formulas, and it makes the perpendicular-height idea unavoidable. A parallelogram and a rectangle can share base and slant length yet have different areas, so this is exactly where students must stop multiplying the two given side lengths. Recognizing it by "Is the height I am using the perpendicular distance between the parallel bases, not the slanted side?" — rather than by familiar numbers — is what lets a student tell it apart from area of a rectangle and area of a triangle and perimeter of a parallelogram in a mixed problem set.

Frequently Asked Questions

What is the Area of Parallelograms formula?

The area of a parallelogram is the product of its base and perpendicular height: A=bhA = bh.

How do you use the Area of Parallelograms formula?

Cut a triangle off one end of the parallelogram and slide it to the other end — you get a rectangle with the same base and height.

What do the symbols mean in the Area of Parallelograms formula?

bb = base, hh = perpendicular height

Why is the Area of Parallelograms formula important in Math?

It is the hinge between rectangle area and the triangle and trapezoid formulas, and it makes the perpendicular-height idea unavoidable. A parallelogram and a rectangle can share base and slant length yet have different areas, so this is exactly where students must stop multiplying the two given side lengths. Recognizing it by "Is the height I am using the perpendicular distance between the parallel bases, not the slanted side?" — rather than by familiar numbers — is what lets a student tell it apart from area of a rectangle and area of a triangle and perimeter of a parallelogram in a mixed problem set.

What do students get wrong about Area of Parallelograms?

The procedure for area of parallelograms is the easy part; the trap is using the slanted side as the height. Asking "Is the height I am using the perpendicular distance between the parallel bases, not the slanted side?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

What should I learn before the Area of Parallelograms formula?

Before studying the Area of Parallelograms formula, you should understand: area, shapes.

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