Primary 5 maths · Measurement & time · About 12 minutes
Find areas of composite rectangles, squares and triangles
Find the right-angle relationship before using a dimension. For a composite surface, keep the pieces separate.
Start the interactive lesson →Open practice activity
What you will learn
- Find areas of composite rectangles, squares and triangles
Models used: number sentences, stories, diagrams.
Before you start
A rectangle with a triangular roof
Split the house shape at the dotted line. We have a rectangle and a triangle.
The dashed line separates the rectangular wall from the triangular roof; it is inside the house.
Split the house shape at the dotted line. We have a rectangle and a triangle.
Base and perpendicular height define the matching rectangle or parallelogram. The triangle’s area is half their product.
The dashed line separates the rectangular wall from the triangular roof; it is inside the house.
The rectangle covers 6 × 4 = 24 square centimetres. The roof covers half of 6 × 2, which is 6.
The dashed line separates the rectangular wall from the triangular roof; it is inside the house.
The two parts meet along an edge, without overlapping. Add their areas.
24 + 6 = 30 cm²
What did the picture help us see?
The two parts meet along an edge, without overlapping. Add their areas.
Worked example: A new example, together
A house-shaped figure has a 6 cm by 3 cm rectangle and a triangular roof with base 6 cm and height 1 cm. Find its area.
Find the right-angle relationship before using a dimension. For a composite surface, keep the pieces separate.
Two matching triangles make a rectangle or parallelogram with the same base and height.
Use the perpendicular height, not a sloping edge. Triangle area = half of base × perpendicular height.
Use the perpendicular height, not a sloping edge. A house-shaped figure has a 6 cm by 3 cm rectangle and a triangular roof with base 6 cm and height 1 cm. Find its area.
21 cm²
Triangle area = half of base × perpendicular height.
Use the perpendicular height, not a sloping edge. Rectangle: 6 × 3 = 18 cm²; triangle: 6 × 1 ÷ 2 = 3 cm².
Use the perpendicular height, not a sloping edge. Add the non-overlapping areas: 21 cm².
Use the perpendicular height, not a sloping edge. Check the result against the question we started with.
The two parts meet along an edge and do not overlap.
We found 21 cm². Two matching triangles make a rectangle or parallelogram with the same base and height.
Use the perpendicular height, not a sloping edge.
Common mistakes to discuss
- Using the outside measurements only. Split the figure into parts, find each part, then combine. A missing side is found from the sides facing it.
Check your understanding
- Find areas of composite rectangles, squares and triangles
- connect triangle area to a matching base and perpendicular height
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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