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Question

Find the area of the adjoining figure. Given :AB=12 cm,AC=13 cm,DE=FG=5 cm,EF=10 cm and GD=4 cm.
188227.JPG

A
88 sq. cm
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B
98 sq. cm
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C
80 sq. cm
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D
75 sq.cm
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Solution

The correct option is A 88 sq. cm
Given :
AB=12 cm,AC=13 cm,DE=FG=5 cm,EF=10 cm and GD=4 cm
ABC is a right angled triangle at B
AC2=AB2+BC2 .......... [By Pythagoras theorem]
132=122+BC2
BC2=169144
BC2=25
BC=5 cm ........ (ii)
In trapezium DEFG, DM and GN are perpendicular
from DG to EF
Now,
MN=GD=4 and
FN+EM=EFMN
=104=6
FN+EM=6 ......... (iii)
Since, the non parallel sides are equal
FN=EM
FN+EM=2FN=6FN=62
FN=3=EM ........... (iv)
Now, DEM is a right angled triangle.
DE2=DM2+EM2 ........ [By Pythagoras theorem]
52=DM2+32
259=DM2
DM=4
DM=GN=4 ........ (v)
Area of ABCDEFGH=Area(ABCH)+Area(DEFG)
=AB×BC+(DG+EF2)×GN
=12×5+(4+102)×4
=60+28
=88 sq. cm
Thus, Area of adjoining figure is 88 sq. cm
Hence, option A is correct.

360299_188227_ans_3b228190ce2b4b81b101aa753b5d5794.png

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