Areas of parallelograms, triangles and trapeziums · Usually met around P5
Heights of triangles and quadrilaterals
Square to the base, from the base to the opposite corner.
How to do it
Method
Square to the base, from the base to the opposite corner
Thick side as base: drop a square line from the opposite corner
Another way
Extend the base
An obtuse triangle's height can lie outside
In full
Choose a side as the base. From the opposite corner (for a parallelogram or trapezium, from any point on the opposite side), draw a line square to the base, down to it: that line's length is the height. A different base has a different height: every side of a triangle can be a base, so a triangle has three heights. For an obtuse triangle on a short side, the height falls outside the triangle, so extend the base first. Check a height two ways: it is square to the base, and it runs from the base (or the base extended) all the way to the opposite corner or side.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
In which picture is the dashed line the triangle's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Show the answer and working
Answer: D
A height is square to the thick base and runs from it to the opposite corner.
Example 2
The dashed line is the triangle's height for the thick base.
True or false?
Show the answer and working
Answer: True
Check two things: square to the thick side, and reaching from it to the opposite corner.
Example 3
In which picture is the dashed line the trapezium's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Show the answer and working
Answer: A
A trapezium's height is the square line between its two parallel sides.
Practise it in the game →Areas of parallelograms, triangles and trapeziums · Free to start, unlimited questions, no download