Area of Triangles

Any triangle fits inside a rectangle of the same base and height, filling exactly half.

The formula that gives

Area is half the base times the height.

The height is not a side

The height is the perpendicular distance from the base to the opposite corner.

Slanting does not change it

Sliding the top corner sideways changes the shape but not the base, height, or area.

Half of the rectangle around it

Any triangle fits inside a rectangle with the same base and height, and takes up exactly half of it. So the area is (base × height) ÷ 2. The halving is not a rule to memorise — it is what the picture shows.

Height means perpendicular height

The height is measured at a right angle to the base, not along a slanted side. For an obtuse triangle the height may fall outside the triangle altogether. Using a slanted side as the height is the commonest error in triangle area.

Any side can be the base

Choose whichever side is convenient, but then use the height perpendicular to that side. All three choices give the same area, which is a useful check when a diagram supplies more than one measurement.

Square units, still

Area is always in square units, whatever the shape. If your triangle answer comes out in centimetres rather than square centimetres, you have found a length, not an area — probably a perimeter.