# Deriving formula for area of a trapezium

From Karnataka Open Educational Resources

### Learning objectives

- The trapeium contains two parallel sides and two non-parallel sides.
- The area of trapezium is found by viewing it as a parallelogram.
- The area of trapezium is 1/2(a+b)h where a and b are its parallel sides and h is the perpendicular distance between them.
- The perimeter of a trapezium is obtained by sum of its 4 sides.

### Notes for teachers

- The area of most figures can be expressed in terms of its dimensions.
- The area of most composite figures can be calculated using the area of primary figures.

### Activity No # 1.Deriving formula for area of a trapezium

- Estimated Time: 20 minutes.
- Materials/ Resources needed : Laptop, geogebra file, projector and a pointer.
- Prerequisites/Instructions, if any

- The students should know a parallelogram and formula to find its area.
- They should know the trapezium and its properties.

- Multimedia resources: Laptop
- Website interactives/ links/ / Geogebra Applets: This geogebra file has been taken from :www.geogebratbe.org

- Process:

- The teacher can initially discuss about a trapezium.
- She can then reiterate that formula for area of certain composite figures can be found by converting them into known simple figures.
- Here the trapezium is converted into a parallelogram.
- Area of parallelogram is then deduced.

- Developmental Questions:

- What is a trapezium ?
- Name its two parallel sides.
- What is meant by the height of the trapezium ?
- After cutting the trapezium exactly in the centre what would be the new height ?
- What is the length of the new parallelogram formed ?
- What is the formula to find the area of a parallelogram ?
- What is the area of this parallelogram formed from a trapezium ?

- Evaluation:

- Explain the sequence of steps involved in deriving the formula for the area of a trapeium.

- Question Corner:

- Write down the steps involved in deriving the formula for area of trapezium.