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

 * 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.