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

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

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

Prerequisite Knowledge

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

Theory

1. 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.
2. Area of parallelogram = Base x Height
   1. Parallelograms on the same base and between the same parallels are equal in area.
   2. 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.(see Fig. 19.2)
   
3. Now, place both trapeziums on cardboard, (see Fig. 19.3)
   

Demonstration

1. In Fig. 19.3, figure 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.

Application
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 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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