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To find a triangle's area, multiply its base by its perpendicular height and divide by two. The important first step is choosing a matching base and height. A sloping side is not automatically the height, even when its length is printed beside the diagram.
This Primary 5 Mathematics guide connects the formula to rectangles, works through original numerical examples and checks common mistakes. Start with a right-angled triangle before trying a diagram whose height lies inside or outside the triangle. Use the right-angle relationship rather than the apparent orientation on the page.
Valour Primary's 2026 Mathematics overview lists triangle area for P5 Standard. MOE's syllabus updated October 2025 is the national reference, but its direct download presented a verification screen. These are original teaching examples, not official assessment questions or a complete syllabus audit. Foundation learners should follow their applicable level sequence.
Area measures the surface inside a figure. Perimeter measures the distance around its boundary. For lengths measured in centimetres, area is recorded in square centimetres, cm², while perimeter is recorded in centimetres, cm.
A triangle with a base of 8 cm and a height of 5 cm does not have an area of 13 cm². Adding two lengths does not measure its surface. Nor can its perimeter be found from those two measurements alone: the height may not be a boundary side.
Imagine an 8 cm by 5 cm rectangle. Its area is 8 × 5 = 40 cm². A diagonal from one corner to the opposite corner divides it into two congruent triangles, each with half the rectangle's area.
Each triangle therefore has area 40 ÷ 2 = 20 cm². This right-triangle example explains the factor of one-half. The general triangle formula uses the same base-and-perpendicular-height relationship, including triangles that are not right-angled.
Choose one side as the base. The matching height is the perpendicular distance from the opposite vertex to the straight line containing that base. Look for a right-angle marker or explicit information establishing perpendicularity.
Rotating a diagram does not change the area. A base can appear vertical or slanted on the page. What matters is the right angle between the base line and its matching height, not whether the height looks upright.
A triangle has a base of 12 cm and a perpendicular height of 7 cm. Area = 12 × 7 ÷ 2 = 42 cm². Write the formula and substitute the two matching measurements before calculating.
Check with the related rectangle: 12 × 7 = 84 cm², so the triangle's area is half of that value. An answer of 84 cm² would suggest that the final division by two was missed.
Suppose a diagram identifies a 10 cm base, a 6 cm perpendicular height and an 8 cm sloping side. Use 10 × 6 ÷ 2 = 30 cm². The sloping side is not the height corresponding to the 10 cm base.
For some triangles, the perpendicular from the opposite vertex meets an extension of the base outside the triangle. That perpendicular distance still supplies the height. Do not measure an unscaled drawing with a ruler to invent a missing value.
Two triangles with the same base length and the same perpendicular height have equal areas even if their shapes look different. If both have base 9 cm and height 4 cm, each area is 9 × 4 ÷ 2 = 18 cm².
Sharing the same base alone is insufficient. A triangle with height 8 cm has twice the area of one with height 4 cm when the base length is unchanged. Name both conditions before concluding that areas are equal.
- Find the area when the base is 6 cm and the perpendicular height is 4 cm.
- Find the area when the base is 15 m and the perpendicular height is 8 m.
- A triangle has base 14 cm, perpendicular height 5 cm and another side 9 cm. Which two values belong in the area calculation?
- Two triangles share a base length of 10 cm. Their heights are 3 cm and 6 cm. Compare their areas.
Answers: 1. 12 cm². 2. 60 m². 3. Use 14 and 5: area = 35 cm². 4. The areas are 15 cm² and 30 cm²; the second is twice the first. State square units for each area.
If the child chooses the wrong measurement, practise marking matching base-height pairs before calculating. If the relationship is clear but arithmetic is uncertain, halve an even factor first: 14 × 5 ÷ 2 can be calculated as 7 × 5.
Check the measurement pair, the division by two and the square unit. A correct formula helps only when the values substituted into it describe the triangle's actual base and perpendicular height.