# Estimating the area under a curve - Higher

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.

### Example

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:

A

B

C

D

E

F

G

The total area is , so the sledge travelled approximately 131.5 m.

## Understanding the meaning of the area

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.

### Example

The units of the area will be .

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