The idea in brief. Mark the base in units before calculating any area. Triangles with the same tip and bases on the same line have the same height, so their areas follow their bases. The figure can then be read with the Ratio chapter's unit chain, and the requested measurement receives its unit only on the last line. In the lesson. The last line is the one that answers it.
Lesson video, with the working
Units on the figure
5 min 16 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
In triangle ABC, D is a point on BC. The ratio of BD to DC is 2 : 3. The area of triangle ABC is 60 cm². Find the area of triangle ABD.
Area of triangle ABD = 2 × 12 = 24 cm²
Ans: 24 cm²
Example 1
ABCD is a rectangle. E is a point on AB. AE is 3 times as long as EB. The area of triangle AED is 36 cm². Find the area of the rectangle ABCD.
Area of ABCD = 4 units × AD = 4 × 24 = 96 cm²
Ans: 96 cm²
Example 2
The figure is made up of a square ABCD and a triangle CDE joined along DC. The angle at D is a right angle. DE is twice as long as DC. The area of the whole figure is 512 cm². Find the length of DC.
DC × DC = 512 ÷ 2 = 256 so DC = 16 cm
Ans: 16 cm
How to solve it
Mark the base in units before any area: B D to D C is 2 to 3, so the whole base is 5 units.
Triangles with the same tip and bases on one line have the same height, so their areas follow their bases.
Share the known area over the units: 5 units is 60 square centimetres, so 1 unit is 12 square centimetres.
Pick out the units you want: triangle A B D is 2 units, which is 24 square centimetres.
Check what the last line gives. If it is an area, like D C times D C, take the square root for the length.
D C times D C is an area. The question asked for a length. The last line is the one that answers it.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
triangles JKM and JML have the same height from J, so their areas follow KM and ML
KL = 3 + 4 = 7 units
3 units = 27
1 unit = 27 ÷ 3 = 9
area of triangle JKL = 7 x 9 = 63 cm²
Answer: 63 cm²
For parents
How do you solve triangle area ratio questions in P6?
When triangles share a tip and their bases lie on one line, they have the same height, so their areas follow their bases.
What your child learns here
When triangles share a tip and their bases lie on one line, they have the same height, so their areas follow their bases. This Primary 6 page applies the ratio outcomes to area of triangle, an exam-style use of both topics.
Recognise triangles with the same height: same tip, bases on one straight line.
Mark the base in units from the given ratio, so a base cut 2 : 3 is 5 units in all.
Share a known area across the units, then pick out the units asked for.
Go the other way: use two areas to find the ratio of the bases, then turn the ratio into a length.
Does the answer make sense?
Triangles sharing a tip with bases on one line have the same height, so the one on the longer base has the larger area. When your child's answer is one part of a figure, it must be smaller than the whole; when it is the whole, larger than every part given.
How to practise these questions
The Basic questions train that triangles with the same height have areas in the same ratio as their bases. Intermediate questions add rectangles and squares joined to triangles, and turning an area ratio back into a length. Challenge questions cut a side into several equal parts, or give one shape as a fraction of another before asking for the whole. When units on a figure stop making sense, read the written step-by-step solution together.
Questions parents ask
Why do triangles with the same height have areas in the ratio of their bases? Area of triangle is ½ × base × height. If the height is the same, only the base changes, so the areas grow and shrink with the bases.
What does units mean on the figure? Units are equal parts used to show a ratio, the same idea as in the Ratio chapter. A base cut 3 : 1 is 4 units long, and each unit of base carries the same share of the area.
Is this a ratio topic or an area topic? Both. It uses the Primary 6 ratio outcome on dividing a quantity in a given ratio together with area of triangle.
