Cutting a triangular piece from one end of a parallelogram and moving it to the other end forms a rectangle with the same base and perpendicular height. Therefore its area is bh. A triangle with that base and height has half this area. A trapezium with parallel sides a,b and perpendicular height h has area 12(a+b)h. Two congruent copies form a parallelogram of base a+b and height h. The height is the distance between the parallel lines, not a sloping side. Example A trapezium has parallel sides 8 cm and 14 cm, with perpendicular height 5 cm. Its area is 12(8+14) x 5=55 cm2. A parallelogram with base 14 cm and the same height has area 70 cm2. For an obtuse triangle or a strongly sloping parallelogram, the height may meet an extension of the base. The same area formula still applies.

Cutting a triangular piece from one end of a parallelogram and moving it to the other end forms a rectangle with the same base and perpendicular height. Therefore its area is \(bh\). A triangle with that base and height has half this area.

A trapezium with parallel sides \(a,b\) and perpendicular height \(h\) has area \(\dfrac12(a+b)h\). Two congruent copies form a parallelogram of base \(a+b\) and height \(h\). The height is the distance between the parallel lines, not a sloping side.

A trapezium has parallel sides 8 cm and 14 cm, with perpendicular height 5 cm. Its area is \(\dfrac12(8+14)\times5=55\text{ cm}^2\). A parallelogram with base 14 cm and the same height has area \(70\text{ cm}^2\).

For an obtuse triangle or a strongly sloping parallelogram, the height may meet an extension of the base. The same area formula still applies.

Perpendicular height and area

Perpendicular height and area