Mathematics
Areas of Parallelograms and Trapeziums
Updated Oct 28, 2026
Use perpendicular height with parallel-sided shapes.
What you’ll learn
Use perpendicular height with parallel-sided shapes.
ប្រើកម្ពស់កែងក្នុងរូបប្រលេឡូក្រាម និងត្រាប៉ែស។
Meaning and use
A parallelogram has two pairs of parallel sides. A trapezium in this lesson has a pair of parallel sides whose lengths are a and b. The height is the perpendicular distance between the parallel lines. A sloping side is not usually the height.
ប្រលេឡូក្រាមមានជ្រុងទល់មុខស្របគ្នា។ ត្រាប៉ែសក្នុងមេរៀននេះមានបាតស្របពីរ a និង b។ កម្ពស់ជាចម្ងាយកែងរវាងបន្ទាត់ស្រប។
Formulas
Parallelogram
\[A=bh\]
Trapezium
\[A=\frac12(a+b)h\]
Symbols and units
| Symbol | Meaning | Unit or restriction |
|---|---|---|
| A | Area | Square length unit |
| b | Parallelogram base, or one parallel trapezium side | Length unit |
| a | Other parallel trapezium side | Same length unit |
| h | Perpendicular height | Same length unit |
Conditions and limits
- For the trapezium formula, a and b must be the parallel sides.
- All lengths must use the same unit.
- កម្ពស់មិនចាំបាច់ស្មើជ្រុងទ្រេត។
Worked examples
A parallelogram
Base is 9 cm and perpendicular height is 4 cm.
- Use \(A=bh\).
- Calculate \(9\times4=36\) cm².
36 cm²
គុណបាតនឹងកម្ពស់កែង។
A trapezium
Parallel sides are 6 m and 10 m; height is 3 m.
- Average the parallel sides: \((6+10)/2=8\) m.
- Multiply by height: \(8\times3=24\) m².
24 m²
រូបមន្តយកមធ្យមប្រវែងបាតទាំងពីរ គុណនឹងកម្ពស់។
Common mistakes
| Instead of | Use | Why |
|---|---|---|
| Trapezium area = ab × h. | Trapezium area = (a + b)h/2. | Use the average of the parallel sides. |
| Use the sloping side as h in every parallelogram. | Use the perpendicular height. | The formula requires a 90° distance to the base. |
Practice
Solve these before revealing the worked solutions. Include units where relevant.
សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។
- Parallelogram base 8 cm, height 5 cm: find area.
- Trapezium parallel sides 4 and 8 cm, height 5 cm: find area.
- Why must a and b be identified before substitution?
Answers and steps
Show solutions / បង្ហាញដំណោះស្រាយ
-
40 cm²
8 × 5 = 40.
-
30 cm²
(4 + 8)/2 × 5 = 30.
-
They are the parallel sides, not any two sides.
The formula depends on that geometric relationship.
Quick recap
- Use perpendicular height.
- Identify the two parallel trapezium sides.
- Area has square units.