Q. 53.6( 22 Votes )

# In the given figure, AB||DC and DA AB If cm, cm, cm and CL AB the area of trap. ABCD is

A. 84 cm^{2}

B. 72 cm^{2}

C. 80 cm^{2}

D. 91 cm^{2}

Answer :

Given:

AB||DC, DA AB and CL AB

cm

cm

cm

Therefore here AL = DC

That is AL = 7 cm

Hence LB = AB – AL = 13 – 7 = 6cm

In LCB using Pythagoras theorem

BC^{2} = BL^{2} + CL^{2}

10^{2} = 6^{2} + CL^{2}

100 = 36 + CL^{2}

CL^{2} = 100 – 36

CL^{2} = 64

CL = 8

Here CL = AD = height of the trapezium

Therefore height = 8 cm

Now,

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

Therefore Area of trapezium = × (7 +13) × 8 = 80 cm^{2}.

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