Q. 74.5( 22 Votes )
Find the area of
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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