# <span lang="EN-US

Area of whole figure = ar || ABCD + ar || FGHI + ar DCIF + ar DEF + area semicircle

CD = 8 cm, BP = HQ = 4 cm, DE = EF = 5 cm, CI = 8 cm

ar ABCD = ar FGHI = base × height

ar ABCD = ar FGHI = BP×DC

ar ABCD = ar FGHI = 4×8

ar ABCD = ar FGHI = 32 cm2 eqn1 and eqn2

ar DCIF = area of square = side×side

ar DCIF = DC×CI

ar DCIF = 8×8

ar DCIF = 64 cm2 eqn3

Consider ∆DEF, EFDF and ∆DEF is isosceles

So, FL = LD

FL = LD = 4 cm

In ∆DEL, DLE = 90°

52 = EL2 + 42 (putting the values)

25 = EL2 + 16

25 – 16 = EL2

EL2 = 9

EL = 3 cm

Area of ∆DEF = 4×3

Area of ∆DEF = 12 cm2 eqn4

R = 4 cm

Area of semicircle = 3.14×8

Area of semicircle = 25.12 cm2 eqn5

Area of whole figure = eqn1 + eqn2 + eqn3 + eqn4 + eqn5

Area of whole figure = 32 + 32 + 64 + 12 + 25.12

Area of whole figure = 165.12 cm2

Area of the whole figure is 165.12 cm 2.

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