Find the area of the adjoining figure. Given :AB=12cm,AC=13cm,DE=FG=5cm,EF=10cm and GD=4cm.
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 A88 sq. cm Given : AB=12cm,AC=13cm,DE=FG=5cm,EF=10cm and GD=4cm △ABC is a right angled triangle at B ∴AC2=AB2+BC2 .......... [By Pythagoras theorem] ⟹132=122+BC2 ⟹BC2=169−144 ⟹BC2=25 ∴BC=5cm ........ (ii) In trapezium DEFG,DM and GN are perpendicular from DG to EF Now, MN=GD=4 and FN+EM=EF−MN =10−4=6 ∴FN+EM=6 ......... (iii) Since, the non parallel sides are equal ∴FN=EM FN+EM=2FN=6⟹FN=62 ∴FN=3=EM ........... (iv) Now, △DEM is a right angled triangle. ∴DE2=DM2+EM2 ........ [By Pythagoras theorem] ⟹52=DM2+32 ⟹25−9=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