The area under a curve can be estimated by dividing it into triangles, rectangles and trapeziums.
If we have a speed-time or velocity-time graph, the distance travelled can be estimated by finding the area.
The velocity of a sledge as it slides down a hill is shown in the graph.
Find the distance travelled by the sledge over its 30-second journey.
Vertical lines every 4 seconds along the horizontal axis have been added and points joined to make triangles, rectangles or trapeziums that approximate to the curve.
The areas of the shapes are:
The total area is , so the sledge travelled approximately 131.5 m.
Page 1 showed how the units can be used to identify the meaning of the gradient: by dividing the vertical axis units by the horizontal axis units.
The meaning of the area under a graph can be found by multiplying the units.
For example, for the velocity-time graph above, .
So the area represents distance in metres.
The units of the area will be .