The parallel sides of a trapezium are 20cm and 32cm. Its non-parallel sides are 10cm each. The area of the trapezium is

# The parallel sides of a trapezium are 20cm and 32cm. Its non-parallel sides are 10cm each. The area of the trapezium is

1. A
2. B
3. C
4. D

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### Solution:

Given: diagram of the trapezium
We have PQRS as a trapezium.
First, we have to find the height of the trapezium.
Since PT and QU are altitudes, then the side TU becomes equal in length to side PQ.
Now take Now in triangles PST and QUR, since pairs of two sides are equal in lengths then it is confirmed that the length of the third side will also be equal.
We calculate the length of ST.
That is, Now, Break the side SR in three parts,
Substitute the value of in RHS.
Shift all constants to RHS,
So, the length of side,
we can apply Pythagoras theorem here,
Where, The height of the trapezium is 8cm.
Now we calculate the area of trapezium PQRS,
Where, Area of PQRS    Area of PQRS   Area of PQRS  .
Hence, Option (3) is the correct answer.

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