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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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