Definition of Trapezium :
The definition of trapezium is entirely different in both US and UK.
Definition of Trapezoid :
In the trapezium / trapezoid above, 'a' and 'b' are the lengths of the parallel sides and 'h' is the height.
Formula to Find Area of Trapezium / Trapezoid :
A = (1/2)(a + b)h
Example 1 :
Find the area of the trapezium ABCD shown below.
Solution :
Area of trapezium = (1/2)(a + b)h
Substitute a = 5, b = 12 and h = 4.
= (1/2)(5 + 12)4
= (1/2)(17)4
= 34 cm^{2}
Example 2 :
In a trapezium the measurement of one parallel side two more than the other parallel side and the height is 4 cm. The area of the trapezium is 64 cm^{2}. Find the lengths of the two parallel sides.
Solution :
Let 'a' and 'b' be the two parallel sides.
One parallel side is two more than the other parallel side.
Then,
a = b + 2
Area of the trapezium = 64 cm^{2}
(1/2)(a + b)h = 64
Substitute h = 4 and a = b + 2.
(1/2)(b + 2 + a)4 = 64
(2b + 2)2 = 64
Divide each side by 2.
2b + 2 = 32
Subtract 2 from each side.
2b = 30
Divide each side by 2.
b = 15
Then,
a = b + 2
a = 15 + 2
a = 17
So, the lengths of the two parallel sides are 15 cm and 17 cm.
Example 3 :
The shape of the top surface of a table is a trapezium. Find its area, if its parallel sides are 1 m and 1.2 m and perpendicular distance between 0.8 m.
Solution :
Area of a the top of surface of the table (trapezium) is
= (1/2)(a + b)h
= (1/2)(1.2 + 1)0.8
= (1/2) (2.2)0.8
= 1.1 (0.8)
= 8.8 m^{2}
Example 4 :
The wall is in the shape as shown below has to be painted. If one can of paint covers 0.5 m^{2}, how many cans of paint will be needed, if only one coat of paint is applied ?
Solution :
In the figure shown above, the perpendicular distance between the two sides BC and AB at any point is same, which is 5 cm.
Then, the sides BC and AD are parallel.
In the quadrilateral above, because the two sides BC and AD are parallel, ABCD is a trapezium.
Let 'a' and 'b' be the lengths of two parallel sides and.
a = BC = 5cm
b = AD = AF + FE + ED = 3 + 5 + 4 = 12 cm
Height (h) = 5 cm
Area of the trapezium ABCD is
= (1/2)(a + b)h
Substitute a = 5, b = 12 and h = 5.
= (1/2)(5 + 12)5
= 42.5 m^{2}
One can of paint covers 0.5 m^{2}.
Number of cans of paint required 42.5 m^{2} is
= 42.5 / 0.5
= 425 / 5
= 85
So, 85 cans of paint required to cover the above wall.
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