Area and Perimeter of a Triangle

$A = \frac{1}{2} \times 10 \times 6 = 30 \text{ cm}^2$

$s = (3+4+5)/2 = 6$

$A = \sqrt{6 \cdot 3 \cdot 2 \cdot 1} = \sqrt{36} = 6 \text{ cm}^2$

(This is a right triangle — check: $\frac{1}{2} \times 3 \times 4 = 6$ ✓)

The triangular gable end of a house has a base of 8 m and a height of 3 m.

A builder wants to know how much cladding material to order.

$A = \frac{1}{2} \times 8 \times 3 = 12 \text{ m}^2$

They order 12 m² of cladding, plus around 10 % extra for waste and cutting.

A surveyor measures a triangular plot with a base of 40 m and a perpendicular height of 25 m.

$A = \frac{1}{2} \times 40 \times 25 = 500 \text{ m}^2$

This equals 0.05 hectares. Landowners, planners, and valuers use the area to assess the plot's worth, calculate planning fees, or estimate crop yield potential.

A triangular warning sign has a base of 0.6 m and a height of 0.52 m.

$A = \frac{1}{2} \times 0.6 \times 0.52 = 0.156 \text{ m}^2$

A manufacturer producing 500 such signs needs $500 \times 0.156 = 78 \text{ m}^2$ of reflective sheeting. Calculating this in advance prevents under-ordering and production delays.