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.