Area of a triangle: the missing half
Your child multiplies the base by the height and stops, so the triangle's area comes out twice as big. In composite figures, where a triangle sits next to a rectangle, the mistake is easy to miss because the rectangle part is right. A related slip is giving the perimeter when the question asks for area.
What it looks like
A figure is made up of a rectangle measuring 12 cm by 8 cm and a triangle on top of it. The triangle has a base of 12 cm and a height of 5 cm. Find the area of the figure.
- Area of rectangle: 12 × 8 = 96 cm²
- Area of triangle: ½ × 12 × 5 = 30 cm²
- Area of figure: 96 + 30 = 126 cm²
Why 156 cm² is wrong: The triangle was worked out as 12 × 5 = 60 cm² without the ½, so 96 + 60 = 156.
Why children do it
- Rectangles are learnt first, and "length × breadth" turns into "base × height" for every shape.
- The ½ is at the front of the formula and gets dropped when your child works quickly.
- Area and perimeter are taught together, so the words get swapped when reading fast.
How to fix it at home
- Show why the ½ is there: draw a rectangle, cut it along the diagonal, and you get two equal triangles.
- Ask your child to write the formula in words first, "½ × base × height", before putting in numbers.
- Have your child circle "area" or "perimeter" in the question and write cm² or cm before calculating.
Questions parents ask
Is "half of base times height" enough, or should my child learn the formula?
The words are enough if your child uses them every time. Writing the formula line first is what stops the ½ going missing.
How do I explain area and perimeter in a way that sticks?
Perimeter is the fence around a garden, area is the grass inside it. A fence is measured in cm, grass in cm².
Where it shows up
Other careless mistakes
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