# To find the formula for the area of a trapezium experimentally.

Lets see how to experimentally find the formula for the area of a trapezium. Before conducting the experiment please go through and study the basic concepts of trapezium, parallelogram and area of quadrilaterals.

## Materials Required

1. Cardboard
2. Thermocol
3. Geometry box
4. Drawing sheets
5. Scissors

### Prerequisite Knowledge

1. Concept of a trapezium.
2. Area of a parallelogram.

### Theory

A quadrilateral in which one pair of opposite sides are parallel and one pair of opposite sides are non-parallel, is called a trapezium. In the image below, ABCD is a trapezium, in which AB||CD and AD, BC are non-parallel. If two non-parallel sides of a trapezium are equal, then it is called an isosceles trapezium.

#### Area of parallelogram = Base x Height

Parallelograms on the same base and between the same parallels are equal in area. If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.

### Procedure

1. Take a cardboard piece of suitable size and by using adhesive, paste a drawing sheet on it.

2. By using thermocol sheet, cut out two congruent trapeziums of parallel sides x and y units with h units altitude.

3. Now, place both trapeziums on cardboard.

### Demonstration

1. In the image above, image is formed by placing, both trapeziums together is a parallelogram.

2. Base of parallelogram = (x + y) units and corresponding altitude = h units.

3. Now, Area of trapezium = ½ (Area of parallelogram) = ½ (Base of parallelogram x Corresponding altitude) = ½[(x + y) x h]

Hence, area of trapezium = ½ x (x + y) x h = ½ x (Sum of parallel sides) x Altitude

Here, area is in square units.

### Observation

Lengths of parallel sides of the trapezium = ………….. , ……………

Length of altitude of the parallelogram = ……………

Area of the parallelogram = ……………

Area of the trapezium = ½ (Sum of …… sides) x ………….

### Result

We have verified experimentally the formula for the area of a trapezium.

### Applications

This concept is used in:

1. finding the formula for area of a triangle, in coordinate geometry.

2. deriving the area of a field which can be split into different trapeziums and right triangles.

### Viva Voce

Question 1: How will you define a trapezium?
Answer: Trapezium is a quadrilateral in which one pair of opposite sides are parallel and the other pair of sides are non-parallel.

Question 2: In a trapezium ABCD, if AB||CD, then which pair of angles are supplementary?
Answer: ∠A and ∠D, ∠B and ∠C are supplementary pairs of angles.

Question 3: Are the opposite angles of trapezium supplementary?
Answer: No, the opposite angles of a trapezium are not supplementary.

Question 4: “Congruent trapeziums have unequal area”. Is this statement true?
Answer: No, because they have equal area.

Question 5: How will you find the area of a parallelogram?
Answer: Area of parallelogram = Base x Altitude to the base.

Question 6: Write the condition that any trapezium should be an isosceles trapezium.
Answer: The condition that any trapezium should be an isosceles trapezium if and only if nonparallel sides of a trapezium are equal.

Question 7: If we take any two points E and F on the line AS of trapezium ABCD such that AB||CD, then check whether the area of △CED and △CFD are equal.
Answer: We know that the area of two triangles on the same base and between two parallel lines are equal. Here, CD is base, points E and F are on the parallel line AB, then area of triangles, △CED and △CFD are equal.

Question 8: Is it correct that every parallelogram is a trapezium?

Question 9: Is it true that sum of all the angles of a parallelogram and trapezium are equal?
Answer: Yes, we know that the sum of all angles of a quadrilateral is 360°. Here, parallelogram and trapezium are quadrilateral.

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