Year 7 · Mathematics · Measurement
Area of triangles and parallelograms
Develop and use formulas for the area of rectangles, triangles and parallelograms, and find the area of shapes made from these.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.
Learning goals
Learners will
- Use the formula for the area of a rectangle.
- Understand why the area of a triangle is half of base × height.
- Calculate the area of parallelograms and composite shapes.
Success looks like
- I can identify the base and the perpendicular height of a triangle or parallelogram.
- I can calculate the area of a triangle using A = ½ × b × h.
- I can calculate the area of a parallelogram using A = b × h.
- I can split a composite shape into simpler shapes to find its area.
The big idea
The area of a rectangle is length × width. Writing this as a formula with b for base and h for height gives A = b × h.
A parallelogram can be rearranged into a rectangle. Cut a right-angled triangle off one end and slide it to the other end. The new rectangle has the same base and the same perpendicular height, so the area of a parallelogram is also A = b × h.
The height must be the perpendicular height, measured at right angles (90°) to the base. The slanted side of a parallelogram is not the height. Using the slanted side gives an area that is too big.
Any triangle is exactly half of a parallelogram (or rectangle) with the same base and height. Draw a triangle, make a copy, rotate it and join them, and you get a parallelogram. That is why the area of a triangle is A = ½ × b × h.
A composite shape can be split into rectangles, triangles and parallelograms. Find the area of each part and add them together. Sometimes it is easier to find a larger area and subtract the part that is missing.
Always include square units in your answer, such as cm² or m². Also remember that 1 m² = 10 000 cm², because a 1 m square is 100 cm by 100 cm.
Worked examples
Area of a triangle
A triangle has a base of 10 cm and a perpendicular height of 6 cm. Find its area.
- Use A = ½ × b × h.
- A = ½ × 10 × 6.
- 10 × 6 = 60, and half of 60 is 30.
Answer: The area is 30 cm².
Area of a parallelogram
A parallelogram has a base of 8 m, a slanted side of 6 m and a perpendicular height of 5 m. Find its area.
- Use A = b × h, with the perpendicular height, not the slanted side.
- A = 8 × 5 = 40.
- The slanted side length of 6 m is not needed.
Answer: The area is 40 m².
A composite shape
The front wall of a garden shed is a rectangle 6 m wide and 3 m high, with a triangular gable on top that has a base of 6 m and a height of 2 m. Find the total area of the wall.
- Rectangle: A = 6 × 3 = 18 m².
- Triangle: A = ½ × 6 × 2 = 6 m².
- Total: 18 + 6 = 24 m².
Answer: The wall has an area of 24 m².
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
A triangle has a base of 8 cm and a perpendicular height of 5 cm. What is its area?
20 cm² — A = ½ × 8 × 5 = ½ × 40 = 20 cm².
A parallelogram has a base of 9 m, a slanted side of 5 m and a perpendicular height of 4 m. What is its area?
36 m² — A = b × h = 9 × 4 = 36 m². The slanted side is not used.
Which formula gives the area of a triangle?
A = ½ × b × h — A triangle is half of a parallelogram with the same base and height, so A = ½ × b × h.
How many square centimetres are in 1 square metre?
10 000 cm² — 1 m = 100 cm, so a 1 m square is 100 cm × 100 cm = 10 000 cm².
A triangular garden bed has a base of 14 m and a perpendicular height of 9 m. What is its area in square metres?
63 m² — A = ½ × 14 × 9 = 7 × 9 = 63 m².
A rectangular rug is 2.5 m long and 4 m wide. What is its area in square metres?
10 m² — A = 2.5 × 4 = 10 m².
A triangle has an area of 24 cm² and a base of 8 cm. What is its perpendicular height in centimetres?
6 cm — 24 = ½ × 8 × h, so 24 = 4 × h, which gives h = 6 cm.
A rectangular wall is 5 m wide and 3 m high. One tin of paint covers 5 m². How many tins are needed for one coat?
3 — Area = 5 × 3 = 15 m². 15 ÷ 5 = 3 tins.
Watch out for
- Using the slanted side instead of the perpendicular height. Draw the height as a dotted line with a right-angle marker every time.
- Forgetting to halve when finding the area of a triangle. Link the formula to the picture of two triangles making a parallelogram.
- Thinking 1 m² = 100 cm². Draw or build a 1 m square and mark 100 cm along each side to see why it is 10 000 cm².
Tips for parents
- Do the paper-cutting activities. Seeing a parallelogram become a rectangle makes the formula meaningful instead of something to memorise.
- Ask the learner to sketch and label every problem, marking the base and perpendicular height before calculating.
- Use real projects, such as working out how much turf or mulch a garden bed needs.
Go further
- Measure the walls of a room, subtract the areas of the door and windows, and estimate how many tins of paint would be needed.
- On grid paper, draw as many different triangles as you can with an area of 12 square units.
- Investigate the formula for the area of a trapezium by joining two identical trapeziums to form a parallelogram.