Deriving formula for area of a trapezium

Learning objectives

1. The trapeium contains two parallel sides and two non-parallel sides.
2. The area of trapezium is found by viewing it as a parallelogram.
3. 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.
4. The perimeter of a trapezium is obtained by sum of its 4 sides.

Notes for teachers

1. The area of most figures can be expressed in terms of its dimensions.
2. 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

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

1. The students should know a parallelogram and formula to find its area.
2. 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:

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

• Developmental Questions:

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

• Evaluation:

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

• Question Corner:

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