Question

# The parallel sides of a trapezium are 20cm and 10cm. Its non parallel sides are both equal. Each being 13cm. Find the area of the trapezium ?

Hint:

### Draw the parallel line from B parallel to AD which cuts the CD at E .

We get a triangle and parallelogram. we find the area of triangle in both heron's

method and using formula area = ½ b × h and equating we get height h

Now , find the area of Trapezium = ½ height × (sum of lengths of parallel sides).

## The correct answer is: 180 cm2

### Ans :- 180 cm^{2}.

Explanation :-

Step 1:- Given lengths of parallel sides is 10 and 20 cm .

Length of non parallel sides is 13 and 13 cm

We get a triangle and parallelogram ABED

we get BE = 13 cm ; DE = 10 cm (opposites sides of parallelogram )

CE = CD-DE = 20 - 10 = 10 cm .

Step 2:- Equate the areas and find value of height h

Step 3:-Find the area of trapezium

Therefore, Area of trapezium ABCD = 180 cm^{2}.

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