Year 6: Area of parallelograms and triangles
Part of the Year 6 area, volume and measures chapter. Chapter overview · whole chapter on one page
Area of parallelograms and triangles
A parallelogram is a four-sided shape with two pairs of parallel sides. Its area is the base times the perpendicular height. The height is measured straight up from the base, at a right angle to it.
A parallelogram can be cut along its height and moved to make a rectangle with the same base and height. So the area is base × height. The slanted side is not used.
A triangle is half of a parallelogram with the same base and height. So its area is half of base × height, or (base × height) ÷ 2.
Key ideas
- Parallelogram: area = base × perpendicular height.
- Triangle: area = (base × perpendicular height) ÷ 2.
- Use the perpendicular height, not the slanted side.
- Area is measured in square units, such as cm².
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 12 cm, perpendicular height = 8 cm (the slanted side, 10 cm, is not used)
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.12 × 8 = 96
- Write the answer. The area is in square centimetres.96
Check. Cut the triangle off one end and move it to the other: a rectangle 12 cm by 8 cm has the same area, 96 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 10 cm, perpendicular height = 7 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.10 × 7 = 70
- Halve the answer. One triangle is half of the parallelogram.70 ÷ 2 = 35
- Write the answer. The area is in square centimetres.35
Check. Two of these triangles make a parallelogram with area 70 cm², so one triangle is 70 ÷ 2 = 35. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 13 cm, perpendicular height = 6 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.13 × 6 = 78
- Halve the answer. One triangle is half of the parallelogram.78 ÷ 2 = 39
- Write the answer. The area is in square centimetres.39
Check. Two of these triangles make a parallelogram with area 78 cm², so one triangle is 78 ÷ 2 = 39. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Watch out
Common mistake: using the slanted side as the height. The slanted side is always longer than the height. Also, for a triangle, do not forget to divide by 2.
Exam tip
A triangle is half of a rectangle with the same base and height. If the answer is bigger than the rectangle, check your working.
Exercise 9D Areas of parallelograms and triangles
Non-calculatorKey words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 6 cm, perpendicular height = 4 cm
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.6 × 4 = 24
- Write the answer. The area is in square centimetres.24
Check. Cut the triangle off one end and move it to the other: a rectangle 6 cm by 4 cm has the same area, 24 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 9 cm, perpendicular height = 5 cm
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.9 × 5 = 45
- Write the answer. The area is in square centimetres.45
Check. Cut the triangle off one end and move it to the other: a rectangle 9 cm by 5 cm has the same area, 45 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 12 cm, perpendicular height = 7 cm
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.12 × 7 = 84
- Write the answer. The area is in square centimetres.84
Check. Cut the triangle off one end and move it to the other: a rectangle 12 cm by 7 cm has the same area, 84 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 8 cm, perpendicular height = 6 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.8 × 6 = 48
- Halve the answer. One triangle is half of the parallelogram.48 ÷ 2 = 24
- Write the answer. The area is in square centimetres.24
Check. Two of these triangles make a parallelogram with area 48 cm², so one triangle is 48 ÷ 2 = 24. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 5 cm, perpendicular height = 4 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.5 × 4 = 20
- Halve the answer. One triangle is half of the parallelogram.20 ÷ 2 = 10
- Write the answer. The area is in square centimetres.10
Check. Two of these triangles make a parallelogram with area 20 cm², so one triangle is 20 ÷ 2 = 10. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 7 cm, perpendicular height = 6 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.7 × 6 = 42
- Halve the answer. One triangle is half of the parallelogram.42 ÷ 2 = 21
- Write the answer. The area is in square centimetres.21
Check. Two of these triangles make a parallelogram with area 42 cm², so one triangle is 42 ÷ 2 = 21. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 9 cm, perpendicular height = 5 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.9 × 5 = 45
- Halve the answer. One triangle is half of the parallelogram.45 ÷ 2 = 22.5
- Write the answer. The area is in square centimetres.22.5
Check. Two of these triangles make a parallelogram with area 45 cm², so one triangle is 45 ÷ 2 = 22.5. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 15 cm, perpendicular height = 4 cm
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.15 × 4 = 60
- Write the answer. The area is in square centimetres.60
Check. Cut the triangle off one end and move it to the other: a rectangle 15 cm by 4 cm has the same area, 60 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the perpendicular height. Do not use the slanted side.
- Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.base = 10 cm, perpendicular height = 12 cm (the slanted side, 13 cm, is not used)
- Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.10 × 12 = 120
- Write the answer. The area is in square centimetres.120
Check. Cut the triangle off one end and move it to the other: a rectangle 10 cm by 12 cm has the same area, 120 cm². ✓
Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Multiply the base by the height, then divide by 2.
- Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.base = 14 cm, perpendicular height = 9 cm
- Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.14 × 9 = 126
- Halve the answer. One triangle is half of the parallelogram.126 ÷ 2 = 63
- Write the answer. The area is in square centimetres.63
Check. Two of these triangles make a parallelogram with area 126 cm², so one triangle is 126 ÷ 2 = 63. ✓
Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Use the area formula backwards: divide the area by the base.
- Write the formula. Area = base times height.48 = 8 × height
- Divide the area by the base. This undoes the multiplication by the base.48 ÷ 8 = 6
- Write the answer. The height is in centimetres.6
Check. 8 × 6 = 48 cm². ✓
Watch out. Divide the area by the base, not the base by the area.
Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.
Method. Find the area of each triangle, then divide the bigger area by the smaller area.
- Find the area of triangle A. The base is 10 cm and the height is 6 cm.(10 × 6) ÷ 2 = 30 cm²
- Find the area of triangle B. The base is still 10 cm, but the height is 9 cm.(10 × 9) ÷ 2 = 45 cm²
- Divide the area of B by the area of A. This tells us how many times bigger B is.45 ÷ 30 = 1.5
- Write the answer. B is 1.5 times the area of A.1.5
Check. 30 × 1.5 = 45, so the answer is right. ✓
Watch out. The height is the only thing that changes here. Changing the height changes the area in the same way.