Primary 6 Area Study Guide

Primary 6 area in four short steps, each built from area of rectangle and area of triangle. Every step has a figure to move, and worked examples follow.

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What is a composite figure, and how do you find its area?

A composite figure is made of simple pieces, so its area is found piece by piece.

The pieces are squares, rectangles and triangles. They may be joined edge to edge, laid over one another, or folded on top. Find each piece with area of rectangle (length × breadth) or area of triangle (1/2 × base × height). Add the pieces that build the figure up, and subtract any part that is covered or cut off.

In this chapter, your child learns to:

  • find the area covered by two identical shapes that overlap;
  • find the area of a triangle drawn inside a rectangle, and work back to a length;
  • find the area seen from above after paper is folded;
  • share a triangle's area in units when its base is split in a ratio.
Rectangle: 10 × 6 = 60 cm²
Triangle: 1/2 × 10 × 4 = 20 cm²
Whole figure: 60 + 20 = 80 cm²
1

Step 1

How to find the area of overlapping shapes

Two shapes laid over each other count the shared part twice. Find the area of each whole shape first. Adding the two areas counts the overlap once in each shape, so the total is one shared part more than the figure they cover. Subtract the overlap once to get the area covered. Work the other way to find the overlap: the two shapes minus the area covered.

Two identical squares of side 10 cm overlap in a square of side 4 cm. Find the area of the figure they cover.

Tap Next step

10 cmB10 cmA
Square A and square B are the same size. The darker part is where they overlap: it belongs to both squares. Tap Next step.
Try it

Two identical rectangles, each 12 cm by 5 cm, overlap. Together they cover 104 cm². What is the area of the overlap?

Two shapes overlap
2

Step 2

Area of a triangle in a rectangle

A triangle on one side of a rectangle, with its tip on the opposite side, is half the box. Area of a triangle is half of base times height. The height is measured at a right angle to the base, so when the base is one side of a rectangle, the height is the other side. Write the rule on its own line, then put in the measurements. To find a missing side, double the area, then divide by the base.

ABCD is a rectangle. AB is 18 cm and BC is 10 cm. E is a point on DC. Find the area of triangle ABE.

Tap Next step

ABCDE18 cm10 cm
Triangle ABE stands on side AB of the rectangle, with its tip E on the opposite side DC. Tap Next step.
Try it

ABCD is a rectangle. AB is 14 cm. E is a point on DC. Triangle ABE has an area of 63 cm². Find the length of BC.

Triangles inside a rectangle
3

Step 3

Folded paper area: what is seen from above

Folding moves paper on top of itself, so less of it can be seen. Find the area of the whole sheet before folding. The folded piece, the flap, now lies on top of the sheet, so the area seen from above is the area of the strip minus the flap. Count one flap for each fold: with both ends folded in, subtract two flaps.

A strip of paper 26 cm by 8 cm has one end folded over. The folded piece is 6 cm long. Find the area seen from above.

Tap Next step

26 cm8 cm6 cm
The strip is flat. The dashed line is where it will fold, 6 cm from the end. Tap Next step.
Try it

A strip of paper is 24 cm by 5 cm. Both ends are folded in by 4 cm each, and the flaps do not meet. Find the area seen from above.

Folded paper
4

Step 4

Triangle area ratio: units on the base

Triangles with the same height share area in the same ratio as their bases. Look for triangles with the same tip and their bases on one straight line: they have the same height. Each area is half of its own base, times that same height, so a base twice as long gives twice the area. Mark the base in units, find what 1 unit of area is, then answer the question.

In triangle ABC, D is on BC and BD : DC = 2 : 3. Triangle ABC is 60 cm². Find the area of triangle ABD.

Tap Next step

?ABCD2 units3 units
D splits BC so that BD : DC = 2 : 3. Tap Next step.
Try it

In triangle PQR, S is on QR and QS : SR = 3 : 1. Triangle PQR is 48 cm². Find the area of triangle PSR.

Units on the figure

Primary 6 area questions, worked step by stepMark the base, height, flap or units on the figure yourself before you open the hint or the working.

Triangle in a boxBasic

PQRS is a rectangle. PQ = 15 cm and QR = 8 cm. T is a point on SR. Find the area of triangle PQT.

Take PQ as the base. The height is the distance from T to PQ.
  1. Area of triangle = 1/2 × base × height
  2. Base = PQ = 15 cm, height = QR = 8 cm
  3. Area of triangle PQT = 1/2 × 15 × 8 = 60 cm²
Answer: 60 cm²
OverlapBasic

Two identical rectangles, each 14 cm by 6 cm, overlap. The part where they overlap is a rectangle 5 cm by 6 cm. Find the area of the figure the two rectangles cover.

Adding both rectangles counts the overlap twice.
  1. Area of 2 rectangles = 14 × 6 × 2 = 168 cm²
  2. Area of overlap = 5 × 6 = 30 cm²
  3. Area covered = 168 − 30 = 138 cm²
Answer: 138 cm²
Folded paperIntermediate

A rectangular strip of paper is 32 cm long and 7 cm wide. Both ends are folded inwards. Each fold is 5 cm long, and the two flaps do not meet. Find the area of the shape seen from above.

There are two folds, so there are two flaps lying on the strip.
  1. Area of strip = 32 × 7 = 224 cm²
  2. Area of 1 flap = 5 × 7 = 35 cm²
  3. Area seen from above = 224 − 35 × 2 = 154 cm²
Answer: 154 cm²
Units on the baseIntermediate

ABCD is a rectangle with an area of 120 cm². E is a point on AB such that AE : EB = 1 : 3. Find the area of triangle AED.

Mark AB in units. Triangle AED has base AE and height AD.
  1. AB = 1 + 3 = 4 units
  2. Area of ABCD = 4 units × AD = 120 cm²
  3. 1 unit × AD = 120 ÷ 4 = 30 cm²
  4. Area of triangle AED = 1/2 × 1 unit × AD = 1/2 × 30 = 15 cm²
Answer: 15 cm²
OverlapChallenge

Two identical squares overlap. The part where they overlap is one quarter of each square. The figure the two squares cover has an area of 112 cm². Find the length of one side of a square.

Let each square be 4 parts. How many parts does the figure cover?
  1. Each square = 4 parts, overlap = 1 part
  2. Figure = 4 + 4 − 1 = 7 parts
  3. 1 part = 112 ÷ 7 = 16 cm²
  4. Area of 1 square = 4 × 16 = 64 cm²
  5. 64 = 8 × 8, so the side is 8 cm
Answer: 8 cm
5

Step 5

Check yourself

Five area questions, one figure each. Nothing is saved, and every reply names the matching question type.

1. ABCD is a rectangle. AB is 12 cm and BC is 9 cm. E is on DC. What is the area of triangle ABE?

2. Two identical squares of side 9 cm overlap in a square of side 3 cm. What area do they cover?

3. A strip of paper 20 cm by 6 cm has one end folded over by 5 cm. It lies flat. What area is seen from above?

4. In triangle ABC, D is on BC and BD : DC = 1 : 2. Triangle ABD is 15 cm². What is the area of triangle ABC?

5. Triangle ABE is drawn in rectangle ABCD, with E on DC. Its area is 70 cm² and AB is 20 cm. What is BC?

0/5
Answer all five to see where to practise next.
For parents

Getting the most from this guide. Before your child taps Next step, ask which pieces make up the figure and which part is counted twice or hidden. Then let the figure show it. Each step takes a few minutes, and the slider at the end is for trying other numbers.

In area questions, ask your child to write area of triangle = 1/2 × base × height before any numbers, and to say how many copies of a piece are being subtracted: one overlap, or one flap for each fold. Keeping cm² on every area line makes the working easy to check.

More study guides

Before this: AnglesNext: SolidsPrimary 5 Area of TrianglePrimary 4 Area and Perimeter study guidePrimary 3 Area and Perimeter study guidePrimary 6 Ratio study guide
Lessons and practice

P6 Area lessons and practice

4 lesson videos and 40 questions across four subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →