Question

1. The area of a rectangle ABCD is 486 cm", and its sides AB and BC are
in the ratio 3:2. The AEAB is equilateral while AFD and BGC are
right-angled isosceles triangles. Find the area of the shaded region.

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Answer 1

let the ratio be x

3x and 2x

length =l and breadth=b

area of triangle = lb

486=3x.2x

486=6x^2

486/6=x^2

81=x^2

x=9

3x=27 and 2x=18

in triamgle AEB = 3 sides

=3.27

=81

in trianhle ADF

(AD)^2 +(AF)^2 =(FD)^2

18^2 + 18^2=(BD)^2

324+324=(BD)^2

648=(BD)^2

√648= BD

25.45

area of triangle = sUm of all sides

=61.45

in triangle BCG= 61.45

area of shaded region =486+81+61.45+61.45

=689.9