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Area of a Triangle

Area of a Triangle

The area of a triangle is given by: `frac(1)(2)bh`

Area of a triangle half base x height

where `b` is the distance along the base of the triangle, and `h` is the vertical height of the triangle.

You do not need to know this, but this is why it works:

Copy the triangle, and rotate and place it to form a parallelogram.

The area of a parallelogram = base x vertical height.

The area of a triangle is half of that.

Triangle area proof: triangle

Example 1

What is the area of this triangle?

Area of a triangle 10cm high 8 cm base

Area of a triangle `= frac(1)(2)bh`
  `= frac(1)(2) xx 10 xx 8`
`= 40 cm^2`

Answer: 40cm2

Example 2

A triangle is twice as high as it is wide. If the area of the triangle is 32 cm2, what is the height of the triangle?

Area of Triangle = base x height
Let the base be `x`: `h` `= 2x`
Substitute: 32 `= x xx 2x`
32 `= 2x^2`
Divide both sides by 2: 16 `= x^2`
Square root both sides: 4 `= x`

Answer: 4 cm