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The difference between two parallel sides of a trapezium is 10 cm. The height is 20 cm. If the area is 500 cm┬▓, find the sum of the parallel sides.
40 cm
50 cm
60 cm
70 cm
50 cm
Use the formula A=average┬аof┬аsides├Чheight. Since A=500 and h=20, the sum (a+b) is simply 2├ЧhAтАЛ, which is 2├Ч25=50.
Difference between parallel sides (a - b) = 10 cm, Height (h) = 20 cm, Area (A) = 500 cm┬▓
A=21тАЛ├Ч(a+b)├Чh
Use the formula A=average┬аof┬аsides├Чheight. Since A=500 and h=20, the sum (a+b) is simply 2├ЧhAтАЛ, which is 2├Ч25=50.
Students often try to find the individual values of side 'a' and 'b' using the system of equations, which is unnecessary since the question directly asks for the sum (a + b).
State the Area Formula
The area of a trapezium is given by the formula where a and b are parallel sides and h is the height.
A=21тАЛ├Ч(a+b)├Чh
Substitute the Known Values
Plug the given area A=500 and height h=20 into the equation.
500=21тАЛ├Ч(a+b)├Ч20
Solve for the Sum of Parallel Sides
Simplify the equation: 500=10├Ч(a+b). Dividing both sides by 10 gives the sum.
(a+b)=10500тАЛ=50
B is correct because the calculated sum of the parallel sides is 50 cm.
This concept is a precursor to coordinate geometry where you might need to calculate the area of a polygon using the coordinates of its vertices.
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