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Primary 6 · Area · Question type 9.4

P6 Area: Triangle Area Ratios with Equal Heights

Triangles with the same height have areas in the same ratio as their bases, so mark the base in units before calculating.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Area chapter4 question types · see the chapter

The lesson · 3 minutes 56 seconds

How do you compare triangle areas with equal heights in P6?

Watch: a triangle with its base cut into 2 parts and 3 parts

Another worked example

A worked example

In triangle WXY, Z is a point on XY. The area of triangle WXZ is 24 cm² and the area of triangle WZY is 36 cm². XY is 20 cm. Find the length of XZ.

The working · Six lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. triangles WXZ and WZY have the same height from W, so their areas follow XZ and ZY
  2. XZ : ZY = 24 : 36 = 2 : 3
  3. XY = 2 + 3 = 5 units
  4. 5 units = 20 cm
  5. 1 unit = 20 ÷ 5 = 4 cm
  6. XZ = 2 x 4 = 8 cm

The answer is 8 cm.

Practise · Modelled on top school exam questions

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Find the whole triangle area

Use the base parts and the known triangle area to find the area of the whole triangle.

In triangle JKL, M is a point on KL such that KM : ML = 3 : 4. The area of triangle JKM is 27 cm². Find the area of triangle JKL.

cm²

Show the step-by-step solution
  1. triangles JKM and JML have the same height from J, so their areas follow KM and ML
  2. KL = 3 + 4 = 7 units
  3. 3 units = 27
  4. 1 unit = 27 ÷ 3 = 9
  5. area of triangle JKL = 7 x 9 = 63 cm²

Ans: 63 cm²

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