Q. 104.7( 24 Votes )

# In the given figure, ABCD is a trapezium in which cm,

cm and cm. find the area of the trapezium.

Answer :

Given

AD = 16 cm

BC = 40 cm

AC = 41 cm

ABC = 90

Height = AB =?

Here in ABC using Pythagoras theorem

AC^{2} = AB^{2} + BC^{2}

41^{2} = AB^{2} + 40^{2}

AB^{2} = 41^{2} – 40^{2}

AB^{2} = 1681 – 1600 = 81

AB = 9

We know that area of trapezium is × (sum of parallel sides) × height

Therefore Area of trapezium = × (16 + 40) × 9 = 252 cm^{2}.

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