Area of Triangles & Parallelograms
Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)
What a learner can do afterwards
- Calculate the area of a parallelogram with base 8 cm and height 5 cm
- Calculate the area of a triangle with base 12 cm and height 7 cm
- Explain why the area of a triangle is half the area of a related parallelogram
1 · Read
Area tells you how much flat space a shape covers. You measure it in square units, like square centimetres (cm²). For a parallelogram, the formula is simple: multiply the base by the height. A = b × h.
A parallelogram has a base of 8 cm and a height of 5 cm. Multiply the base by the height: 8 × 5 = 40. The area is 40 cm².
A triangle is different. Two matching triangles fit together to make a parallelogram with the same base and height. So a triangle's area is always half of that parallelogram's area. The formula is A = ½ × b × h.
Always multiply base by height first. Only halve the answer if you are working with a triangle. Keep the units as square centimetres (cm²).
Multiply base by height for a parallelogram; halve that answer for a triangle.
More to read
2.3: Area of Parallelograms
A parallelogram is a slanted rectangle, and its area is still base times height. The height must be perpendicular to the base, not the slanting side. For base 8 cm and height 5 cm, the area is 40 square cm. Cutting the slanted triangle off one end and moving it to the other makes a plain rectangle. That cut and move trick proves the rule with no algebra.
10.6 Area
A triangle is half a parallelogram with the same base and height. Two identical triangles always join into such a parallelogram. So triangle area is half times base times height. A triangle with base 12 cm and height 7 cm covers half of 84, which is 42 square cm. Forgetting the half is the most common slip, so halve last and halve always.
How to Find the Area of a Parallelogram with a Formula
Working backwards finds missing sides. If a parallelogram covers 48 square cm with base 8 cm, divide: 48 / 8 = 6 cm tall. If a triangle covers 42 square cm with base 12 cm, double first: 84 / 12 = 7 cm tall. Division undoes the area rule cleanly. Always check by multiplying back: 8 times 6 is 48, and half of 12 times 7 is 42.
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.