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Primary 5 Area of Triangle study guide: the whole chapter, step by step

About this subtopic

This mixed practice stop brings together 5 topics from Primary 5 Area of Triangle: Base and height, Area of a triangle, One figure, three shapes, Triangles inside a rectangle, Two shapes overlap. Nothing on the question says which topic it comes from, so choosing the method is part of the skill.

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Intermediate

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Question 1 of 8 · Intermediate · free to tryThe figure is made up of triangles PJK and QJK, and Q lies inside triangle…The figure is made up of…

The figure is made up of triangles PJK and QJK, and Q lies inside triangle PJK. JK = 22 cm. PM and QN both meet JK at a right angle, PM = 15 cm and QN = 6 cm. The shaded part is triangle PJK with triangle QJK taken out of it. Find the area of the shaded part.

cm²

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Working

  1. area of a triangle = 1/2 × base × height
  2. triangles PJK and QJK stand on the same base JK
  3. area of triangle PJK = 1/2 × 22 × 15 = 165 cm²
  4. area of triangle QJK = 1/2 × 22 × 6 = 66 cm²
  5. area of the shaded part = 165 − 66 = 99 cm²

Answer: 99 cm²

For parents

How do you solve P5 area of triangle mixed practice questions?

Every question here is a figure made of more than one shape: two triangles on a shared base, a triangle on a rectangle, a triangle whose base has been produced, or two cards overlapping on a board.

What your child learns here

Every question here is a figure made of more than one shape: two triangles on a shared base, a triangle on a rectangle, a triangle whose base has been produced, or two cards overlapping on a board. Your child decides which triangle each area belongs to, which side to use as its base, and which perpendicular line is its height. The questions draw on all three Primary 5 Area of Triangle outcomes: base and height, the area of a triangle, and composite figures.

  • The height of a triangle is the perpendicular from its tip to the line of its base, even when that line has to be produced.
  • A slanting side is not a height unless it meets the base at a right angle.
  • Two triangles on the same base can be added or subtracted as one, using the sum or the difference of their heights.
  • Triangles with the same height have areas in the same ratio as their bases.
  • When two shapes overlap, the area covered is both areas added with the shared part taken away once.
Does the answer make sense?

When a triangle is taken out of another on the same base, the answer can be found a second way. In the shaded band question, the base is 22 cm and the heights are 15 cm and 6 cm, so half of 22 times the difference of 9 cm gives 99 cm², the same as 165 cm² minus 66 cm².

How to practise these questions

All eight questions are Intermediate. Two put two triangles on one shared base, either adding them into a four-sided figure or taking a smaller triangle out of a larger one. Two join a triangle to a rectangle, one with its base inside the rectangle's edge and one where the slant sides are printed but only one line is the height. One produces a side of a triangle to reach its height. One finds a whole triangle from a quarter of its base. Two start somewhere else: a sheet of paper whose length comes from two perimeters, and two cards overlapping on a notice board. Ask your child to trace each triangle's base and height before writing any number.

Questions parents ask

What if the height falls outside the triangle? Produce the base, and the height meets that longer line at a right angle. The area is still half of the base times that height, using the triangle's own base, not the produced line.

Why does a figure print lengths that are not needed? Slant sides are often printed beside the true height. Choosing the perpendicular one is part of the Primary 5 outcome on base and height.

Should my child add parts or take parts away? Add when shapes are joined edge to edge. Take away when a shape is cut out of a larger one, or when an overlap would be counted twice.