Finding Areas under Graphs
How do I estimate the area under a graph?
- To find an estimate for the area:
- Split area into vertical strips
- Draw straight lines at top of strips
- Find area of strips (trapeziums) using Area = ½(a + b)h
- Add the areas
How do I know if my answer is an underestimate or an overestimate?
- A common exam question is to ask if your estimate of the area is an underestimate or an overestimate
- To answer this, simply look at the straight lines joining the tops of your strips
- If the straight lines are below the curve, it is an underestimate
- If the straight lines are above the curve, it is an overestimate
- At GCSE, the lines will all be below or all be above the curve- though it may be difficult to tell which for some strips
Examiner Tip
- This is particularly useful when working with Speed-Time and Distance-Time graphs if they are curves and not straight lines.
Worked example
