Question

# The difference between two parallel sides of a trapezium is 4 cm.The perpendicular distance between them is 19 cm.Find the area of the trapezium and find the length of parallel sides.

Solution

## Let the two parallel sides of the trapezium be $$a$$ cm and $$b$$ cm.Given that difference between the two parallel sides is 4 and the perpendicular distance$$(h)$$ is 19$$\Rightarrow a-b=4\quad \longrightarrow (1)$$We know that Area of Trapezium = $$\dfrac { 1 }{ 2 } \times \left( a+b \right) \times h$$Substituting the values of $$h$$ we get,$$\dfrac { 1 }{ 2 } \times \left( a+b \right) \times 19=475$$$$\Rightarrow \left( a+b \right) =\dfrac { 475\times 2 }{ 19 }$$$$\Rightarrow a+b=50\quad \longrightarrow \left( 2 \right)$$Adding (1) and (2),$$a-b=4$$$$\underline { a+b=50 }$$$$-2b=-54$$$$b=\dfrac { 54 }{ 2 } =27$$Putting $$b=27$$ in $$(2)$$ we get$$a+27=50$$$$a=50-27=23$$Two parallel sides are $$27$$ cm and $$23$$ cm.Mathematics

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