Question

Please find the area of the following figure with explanation​.

Answer 1

Solution:

Please refer attachment

AB = BC = CH = HA = 6 cm

ABCH is a Square

Area of square ABCH = Side²

Area of square ABCH = 6² = 24 Cm²

Now ,

HG = AG - AH

HG = 10 cm

then ,

Extend DE & GF to point 'I'

Considering HG = DI = 10 cm

EI = DI - DE

EI = 10 - 6

EI = 4 cm

If HD = HC + CD = 6+6 = 12 cm

then HD = GI

FI = GI - GF

FI = 12 - 5

FI = 7 cm

Now ,

In ∆ EFI,

FI (Base) = 7 cm

EI (Height) = 4 cm

Area of ∆ EFI = $\dfrac{1}{2}\times 4 \times 7$

Area of ∆ EFI = 14 cm²

In rectangle HDIG ,

Area = Length × Breadth

= 10 × 12 cm²

= 120 cm²

Area of Total Figure ABCDEFG = 120+24-14 =120+10

Area of Total Figure ABCDEFG = 130 cm²