Parallelogram area
FoundationArea = base × height.
- Area of a parallelogram = base × height (A = b × h)
- The height is the perpendicular distance, not the slant side
- Cut-and-shift turns it into a rectangle of equal area
1Summary 重點摘要
Area = base × height.
2Vocabulary cards Vocabulary
The bottom edge of the parallelogram, e.g. the 6 cm side.
The perpendicular distance from the top edge to the base — must make a right angle.
Two lines meeting at a 90° right angle.
The amount of flat space a shape covers, in square units.
Area units, e.g. cm², m².
The two tilted sides — they are NOT the height.
Cut along the height and move the triangle to the other side, turning it into a rectangle.
Area = base × height, written A = b × h.
3Step by step Steps
- Step 1: Know the shapeA parallelogram has opposite sides parallel, like a rectangle pushed sideways. Its corners are not right angles, but opposite sides stay equal. Knowing the shape's features helps you pick the right area formula.
- Step 2: Tell base from heightThe base is the 6 cm bottom edge; the height is the perpendicular distance from the top edge, here 4 cm, marked with a right-angle sign. The slant side 5 cm is not the height: perpendicular is what matters, not which side is longer.
- Step 3: Why the formula worksCut off the left triangle along the height and move it to the right: the parallelogram becomes a 6 by 4 rectangle. Only the position changed, so the area is unchanged. That is why area = base × height, the same idea as a rectangle.
- Step 4: Substitute into the formulaPut the base 6 cm and the height 4 cm into the formula: area = base × height = 6 × 4 = 24. Before multiplying, check that the two numbers are a matching pair of base and height.
- Step 5: Use square unitsThe answer is 24 square centimetres, written 24 cm², never 24 cm. Area measures the size of a flat surface, so it always takes square units; centimetres alone measure length. With the wrong unit, even the right number is incomplete.
- Step 6: Match each base with its heightEvery base pairs with the height perpendicular to it: base 6 with height 4 gives 24; using the slant side 5 as a base needs its own height 4.8, and 5 × 4.8 = 24 again. Any matching pair works, but the pair must match.
4Diagrams Diagrams
5Worked example Example
Example: a parallelogram flower bed has base 8 cm and height 5 cm (slant side 6 cm). What is its area?
- Write the formula: area of a parallelogram = base × height.
- Pick the matching pair: the height is the perpendicular 5 cm; the slant side 6 cm must not be used.
- Substitute: area = 8 × 5.
- Calculate: 8 × 5 = 40.
- Attach square units: the area is 40 cm².
- Answer: The flower bed has an area of 40 cm². We multiplied the base 8 cm by the perpendicular height 5 cm; the 6 cm slant side is not the height, so the answer 8 × 6 = 48 would be wrong. Area needs square units, so the complete answer is 40 cm², not 40 cm.
6Common mistakes Mistakes
7Quick check Quick check
Q1A parallelogram has base 7 cm and height 3 cm. Area?
Q2Base 10 cm, height 4.5 cm. Area?
Q3Area 36 cm², base 9 cm. What is the height?
Q4Base 5 cm, height 4 cm, slant side 6 cm. Is the area 30 cm²?
Q5When measuring the height, what angle must the ruler make with the base?
8Recap Recap
- Area of a parallelogram = base × height (A = b × h)
- The height is the perpendicular distance, not the slant side
- Cut-and-shift turns it into a rectangle of equal area
- Area units are square units (cm²)
- Each base pairs with its own perpendicular height