Area of a Parallelogram: Base × Height

ME11Area of Parallelograms

A pushed-over rectangle.

A parallelogram is a rectangle leaning sideways — same area formula, no halving.

Slice and slide: parallelogram → rectangle.

9 × 5 = 45 cm²

Area of a parallelogram = base × height (perpendicular height!)

Learn the 3-Step Method

1See the slice-and-slide.

Cut the slanted triangle off one end, slide it to the other — you get a rectangle.

2Multiply base × height.

Same as the rectangle it becomes: 9 × 5 = 45.

9 × 5 = 45

3No halving!

Unlike triangles, parallelograms use the full base × height.

45 cm²

💡 Key IdeaUse the perpendicular height, not the slanted side — exactly like triangles.

Worked Example

A parallelogram has base 12 cm, perpendicular height 4 cm, and slanted side 5 cm. Find its area.

Pick the right numbers

base 12, height 4
ignore the 5 cm slant!

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Multiply

12 × 4 = 48

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✓ Answer

48 cm²

Watch Out! Common Mistakes

Using the slanted side.

A = 12 × 5 = 60 cm² ✕

Wrong! The 5 cm slant is a trap. Use the perpendicular height: 12 × 4 = 48 cm².

Halving like a triangle.

(9 × 5) ÷ 2 = 22.5 cm² ✕

Wrong! No halving for parallelograms — the slice-and-slide makes a FULL rectangle: 45 cm².

Calling any slanted shape a parallelogram.

Check! A parallelogram needs two pairs of parallel sides. A trapezium (one pair) has a different formula.

⬇ Cheat Sheet

AREA OF PARALLELOGRAMS

Area = base × perpendicular height.
Ignore the slanted side length.
No halving (that's triangles).
Slice-and-slide shows why: it becomes a rectangle.

Examples: b9 h5 → 45 cm² · b12 h4 → 48 cm² (slant 5 is a trap!)

📖 Continue Your Journey

✓ ME1 Units of Length ✓ ME2 Converting Length ✓ ME3 Units of Mass ✓ ME4 Converting Mass ✓ ME5 Units of Capacity ✓ ME6 Converting Capacity ✓ ME7 Reading Scales ✓ ME8 Perimeter ✓ ME9 Area of Rectangles ✓ ME10 Area of Triangles ME11 Area of Parallelograms ME12 Compound Shapes ME13 Volume of Cuboids ME14 Telling the Time ME15 Time Calculations ME16 Money Calculations ME17 Imperial and Metric Units ME18 Measurement Problem Solving

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Next Lesson: ME12 Compound ShapesSplit tricky shapes into easy rectangles.

📄 Free printable: Download the Area of Parallelograms cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Area of a parallelogram = base × perpendicular height.
The slanted side is never used in the area calculation.
No halving — slice-and-slide turns it into a full rectangle.
Exam diagrams often print the slant length as a trap.

Frequently asked questions

What is the formula for the area of a parallelogram?

Base × perpendicular height. A parallelogram with base 9 cm and height 5 cm has area 45 cm².

Why doesn't the slanted side matter?

Because slicing the slanted triangle off one end and sliding it to the other turns the parallelogram into a rectangle whose sides are the base and the perpendicular height.

How is this different from a triangle's area?

No halving. A triangle is half its surrounding rectangle; a parallelogram rearranges into a whole one.

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ME10 Area of Triangles