There are 10 small squares in the given figure.
Area of the small square = 1 $c{m}^2$
$\Rightarrow$ Area of the given figure
     = 10 $\times$ Area of one square
     = 10 $\times$ 1 $c{m}^2$
     = 10 $c{m}^2$

Given : Perimeter of the given figure = 15 cm 
Let the length of the third side be x.
Perimeter of a figure = Sum of lengths of its sides = AB + BC + AC
$\Rightarrow$ 15 cm = 6 cm + 5 cm + x
$\Rightarrow$ 15 cm = 11 cm + x
$\Rightarrow$ x = 15 cm - 11 cm
$\Rightarrow$ x = 4 cm
Therefore, the third side is 4 cm long.

Given: The length of the sides of each square is 10 cm. 
For the rectangle formed:
Length = 10 cm + 10 cm = 20 cm
Breadth = 10 cm
Area of the rectangle = Length $\times$ Breadth = $20cm\times 10cm=200c{m}^2$

Area of the given shape = area of the two rectangles
= $(10m\times 5m)+(5m\times 8m)$
= $50m^2+40m^2$
= $90m^2$

In the given figure, we have length = 4 cm and breadth = $\frac{1}{4}$ cm
Area of the figure = length $\times$ breadth
$\Rightarrow$ Area of the given rectangle = 4 cm $\times$ $\frac{1}{4}$ cm = 1 $c{m}^2$

Sum of areas of the triangles will be same as that of the area of the square, it will be like calculating the area of two triangles which forms the square.

Area of the square = Side $\times$ Side

Given: Side = 13 cm

$\therefore$ Area = 13 $\times$ 13 = 169 $c{m}^2$

Area of a square = Side $\times$ Side  
$\Rightarrow$ Side $\times$ Side = 64 $c{m}^2$
When we look at the factors of 16,
64 = 64 x 1
64 = 32 x 2
64 = 16 x 4
64 = 8 x 8
Since the sides have to be equal, it has to be 8 cm long as 8 $\times$ 8 = 64
$\therefore$ Side will be 8 cm long.

1 m = 100 cm.
Hence 1 sq. m $=100\times 100c{m}^2$
$\Rightarrow 0.9m^2=0.9\times 100\times 100=9000c{m}^2\text{( shifting the decimal by 1 place)}$

Decimeter is not a unit of area. Units of area are given as squared units