Area of Parallelograms

Learn how to calculate the area of a parallelogram using the base and height formula.

Intermediate25 minLesson
Printable worksheet

Definition

A parallelogram is a four-sided shape where opposite sides are parallel and equal in length.
To find the area of a parallelogram, we use:
A=b×hA = b \times h
Where:
  • bb is the base (any side of the parallelogram)
  • hh is the height (the perpendicular distance from the base to the opposite side)
Important: The height is NOT the slant side! It must be measured at a right angle (90°) to the base.

Try it now

What is the formula for the area of a parallelogram?

Worked Examples

Find the area of a parallelogram with base b=8b = 8 cm and height h=5h = 5 cm.
1

Write the formula

A=b×hA = b \times h → Area formula
2

Substitute the values

A=8×5A = 8 \times 5 → Plug in base and height
3

Calculate

A=40A = 40 → 4040 cm²

Common Mistakes

Using the slant side instead of the perpendicular height

Why it's wrong: The slant side is the length of the tilted edge, not the vertical distance between parallel sides.

Correct: Always look for the height that forms a 90° angle with the base. It's often shown with a small square symbol.

Forgetting to include square units in the answer

Why it's wrong: Area is always measured in square units because we're measuring two-dimensional space.

Correct: If base and height are in cm, the area is in cm². If in meters, the area is in m².

Multiplying all four sides together

Why it's wrong: Unlike perimeter (which uses all sides), area only needs base and height.

Correct: Use only two measurements: A=b×hA = b \times h

Interactive Visual

Area and perimeter

b = 8h = 4s = 5

Area32

A=b⋅h=8⋅4=32A = b \cdot h = 8 \cdot 4 = 32

Perimeter26

P=2(b+s)=2(8+5)=26P = 2(b + s) = 2(8 + 5) = 26

Cut the triangle off one end and move it to the other: you get a b × h rectangle.

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

18 problems
Problem 1 of 18
Easy
What is the formula for the area of a parallelogram?

Why It Matters

Understanding the area of parallelograms is essential because:
  • Architecture: Parallelogram shapes appear in modern building designs and roof structures
  • Art and Design: Many patterns and tiles use parallelogram shapes
  • Physics: Forces and vectors often form parallelograms (parallelogram law)
  • Foundation for other shapes: The parallelogram formula helps us understand the area of triangles, rhombuses, and other quadrilaterals

Real World Applications

Flooring and Tiles

Some decorative tiles are parallelogram-shaped. Knowing the area helps calculate how many tiles you need.

Example:

A parallelogram tile has a base of 20 cm and height of 15 cm. Each tile covers 20×15=30020 \times 15 = 300 cm² = 0.030.03 m².

1Try It Yourself

You need to cover a floor of 6 m² with parallelogram tiles. Each tile has base 30 cm and height 20 cm.

How many tiles do you need?

Step 1: Write the mathematical expression

First find one tile's area, then divide:

Sail Design

Many sail shapes on boats approximate parallelograms. Calculating sail area is crucial for performance.

Example:

A sail with base 4 m and height 6 m has an area of 4×6=244 \times 6 = 24 m².

2Try It Yourself

A boat needs 30 m² of sail area. The sail base is fixed at 5 m.

What height must the sail be?

Step 1: Write the mathematical expression

Rearrange A=b×hA = b \times h to find hh:

Key Takeaways

  • 1A parallelogram has opposite sides that are parallel and equal
  • 2Area formula: A=b×hA = b \times h (base times height)
  • 3The height must be perpendicular (90°) to the base
  • 4Don't confuse the slant side with the height
  • 5Area is always expressed in square units (cm², m², etc.)

Frequently Asked Questions

The slant side doesn't tell us the actual vertical space inside the shape. Only the perpendicular height measures the true distance between the parallel sides.
The slant side doesn't tell us the actual vertical space inside the shape. Only the perpendicular height measures the true distance between the parallel sides.
Yes! But you must use the height that's perpendicular to that specific base. Different bases have different corresponding heights.
Yes, it's the same formula (A=b×hA = b \times h). A rectangle is actually a special parallelogram where all angles are 90°.

Glossary

Parallelogram
A four-sided polygon with two pairs of parallel sides
Base
Any side of the parallelogram chosen for calculating area
Height
The perpendicular distance from the base to the opposite side
Perpendicular
At a 90-degree angle
Area
The amount of space inside a two-dimensional shape, measured in square units
Today's challengeOne problem, three tries

More in This Topic

Perimeter of Polygons

Elementary20 min

Area of Rectangles and Triangles

Elementary25 min

Area of a Rhombus

Intermediate20 min

Area of Trapezoids

Intermediate20 min