Area of a Parallelogram
Area of a parallelogram.
Formula
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Example
Base 8, height 3: A = 8·3 = 24 square units.
How it works
A parallelogram has the same area as a rectangle with the same base and perpendicular height. If you cut off the triangular part on one side and move it to the other, the shape can be rearranged into a rectangle without changing its area, which is why the formula is base times height. The key is that the height must be the straight-up distance between the parallel sides, not the slanted side length.
When to use it
Use this formula when you need the area of a slanted four-sided shape with two pairs of parallel sides. It appears in geometry problems, design and construction measurements, and any situation where you know the base and the perpendicular height.
Worked example, step by step
A parallelogram has base 12 cm and height 5 cm. Use the formula A = b h Substitute the values: A = 12 × 5 Multiply: A = 60 Final answer: 60 cm²
Common mistakes to avoid
- using the slanted side instead of the perpendicular height
- forgetting to square the units in the final answer
- mixing up base and height when reading the diagram
Did You Know?
A parallelogram has the same area as a rectangle with the same base and height — just slide the slanted piece over.
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