Answer :

Given: A figure ABCDEFGH


BC = FG = 4 cm


AB = HG = 5 cm


CD = EF = 4 cm


ED = 8 cm


ED || AH


AH = 8 cm


Here


ABC and GHF are equal and right angled


AC = AH = ?


In ABC using Pythagoras theorem


AB2 = BC2 + AC2


52 = 42 + AC2


25= 16+ AC2


AC2 = 25 –16 = 9


AC = 3


AH = 3


Area(ABCDEFGH) = area(Rect. ADEH) + 2 X area (ABC)


Area of rectangle = (length × breadth)


Area of triangle = × (base) × (height).


Area(Rect. ADEH) = (DE × AD) = (DE × (AC + AD)) = (8 × (3 + 4)) = 56 cm 2


Area(ABC) = × (BC) × (AC) = × (4) × (3) = 6 cm2


Area(ABCDEFGH) = area(Rect. ADEH) + 2 × area (ABC) = 56 + (2 × 6) = 68 cm2


Area(ABCDEFGH) = 68 cm2.


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