How to teach the area of triangles and parallelograms
Year 7 (ages 12 to 13)
The area formulas for triangles (1/2 x base x height) and parallelograms (base x height) both come from the area of a rectangle. This unit covers applying both formulas and finding a missing dimension when the area is already known.
How to teach it
- Show why a parallelogram's area equals base x height by cutting and rearranging it into a rectangle.
- Show why a triangle's area is HALF of base x height by fitting two identical triangles together to make a parallelogram.
- Practise identifying the base and the PERPENDICULAR height in a diagram, since the height is not always a drawn side.
- Solve for a missing base or height by rearranging the formula (dividing the area by the known dimension) once the standard direction is secure.
- Mix triangle and parallelogram problems together so students practise choosing the right formula each time.
Worked example
Find the area of a triangle with base 10 and height 6 1/2 x 10 x 6 = 30 square units
Common mistakes
- Forgetting to halve the result for a triangle (using the parallelogram formula by mistake).
- Using a slanted side as the height instead of the perpendicular distance from the base.
- Multiplying instead of dividing when finding a missing base or height from a known area.
- Mixing up which dimension is the 'base' when a shape is drawn at an angle.
Frequently asked questions
What is the formula for the area of a triangle?
Area = 1/2 x base x height. A triangle with base 8 and height 5 has area 1/2 x 8 x 5 = 20 square units.
What is the formula for the area of a parallelogram?
Area = base x height (the same as a rectangle, since a parallelogram can be rearranged into a rectangle of the same base and height).
How do you find a missing base or height if you know the area?
Divide the area by the known dimension. If a parallelogram has area 40 and height 8, its base is 40 / 8 = 5.
What year is the area of triangles and parallelograms taught?
In the Australian Curriculum this is a Year 7 skill (AC9M7M01): using established formulas and suitable units to solve problems about the area of triangles and parallelograms.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.