**NCERT Class 9 Maths Lab Manual – Find the Formula for the Area of a Trapezium**

**OBJECTIVE**

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

**Materials Required**

- Cardboard
- Thermocol
- Geometry box
- Drawing sheets
- Scissors
- Adhesive

**Prerequisite Knowledge**

- Concept of a trapezium.
- 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 Fig. 19.1, ABCD is a trapezium, in which AB||CD and AD, BC are non-parallel.

Area of trapezium = ½ (Sum of parallel sides) x Distance between parallel sides (Altitude)

= ½(AB + CD) x DE

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**

- Take a cardboard piece of suitable size and by using adhesive, paste a drawing sheet on it.
- By using thermocol sheet, cut out two congruent trapeziums of parallel sides x and y units with h units altitude.(see Fig. 19.2)

- Now, place both trapeziums on cardboard, (see Fig. 19.3)

**Demonstration**

- In Fig. 19.3, figure formed by placing, both trapeziums together is a parallelogram.
- Base of parallelogram = (x + y) units and corresponding altitude = h units
- 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.

**Application**

This concept is used in

- finding the formula for area of a triangle, in coordinate geometry.
- 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 non-parallel 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 ΔCED and ΔCFD 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, ΔCED and ΔCFD are equal.

**Question 8:**

Is it correct that every parallelogram is a trapezium?

**Answer:**

No

**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.

**Suggested Activity**

Using the above activity, find the area of an isosceles trapezium, if one of its non-parallel side is 5 cm and lengths of two parallel sides are 4 cm and 10 cm.

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