No. of Squares = 7
Area of each square = 7 \(\times\) 7 = 49
\(\therefore\)  Area of 'L' shaped figure = 7 \(\times\)49 = 343 cm²

(i) 4 square tiles horizontally and 4 square tiles vertically.
\(\Rightarrow\) 4 \(\times\) 4 = 16 sq. units.
No. of tiles tilled = 7
No. of tiles required = 16 -7 = 9
(ii) 4 square tiles vertically and 3 square tiles horizontally .
Area \(\Rightarrow\) 4 \(\times\) 3 = 12 sq. units.
No. of tiles filled = 6
(iii) 4 square tiles vertically and 3 square files horizontally.
Area = 4 \(\times\) 3 = 12 sq. units.
No. of tiles filled = 6
Required tiles = 12 - 6 = 6
(iv) 4 square tiles horizontally and 4 square tiles vertically.
Area = 4 \(\times\) 4 = 16 sq. units.
No. of tiles filled = 8
Required tiles = 16 - 8 = 8 

To prove: Square B = 2 (Square A)
Let the side of the square B = 4 cm
P = 4s = 4 \(\times\) 4 = 1.6.cm
Next, The side of the square A = 2 cm
P = 4s = 4 \(\times\) 2 = 8 cm
\(\therefore\) Square B = 16 = 2 (8) = 2 square A
\(\therefore\) Perimeter of square B is twice that of square A.

length = 40 cm
breadth = 20 cm
Side of the square = 10 cm
Area of the rectangle = lb
= ( 40 \(\times\) 20)cm²
= 800 cm²
(side) s = 10cm
Area of a square (S2) = 102 = 100 cm²
No. of square = \(\cfrac { 800 }{ 100 } =8\)

(i) Given :
Perimeter = 12 times 4 cm
= 12 \(\times\) 4 = 48 cm
Area \(\Rightarrow\) Given  = 5 squares
= 5 \(\times\) area of square
= 5 \(\times\) (sider)²
= 5 \(\times\) 42
\(\therefore\)  A = 5 \(\times\) 16 = 80 Cm²
 \(\therefore\) P = 48 cm, A = 80 cm²
(ii) Given :
Perimeter = 4 times 4 cm + 4 times 5cm
= 4 (4) + 4 (5)
= 16 + 20 = 36 cm
Area = 4 triangles + 1 square
= \(4\left( \frac { 1 }{ 2 } bh \right) +1\left( s \right) ^{ 2 }\)
= \(4\left( \frac { 1 }{ 2 } \left( 5 \right) \left( 4 \right) \right) +1\left( { 3 }^{ 2 } \right) \)
= 4 \(\times\) 5 \(\times\) 2 + 9
= 40 + 9 = 49 cm²
(iii) Given :
Perimeter = (50 + 12 + l3 + 40 + 10 +10 + 10 + 5) cm
= 150 cm
= \(\left( lb+\cfrac { 1 }{ 2 } bh+{ s }^{ 2 } \right) { cm }^{ 2 }\)
= \(\left( 50\times 5 \right) +\cfrac { 1 }{ 2 } \times 12\times 5+{ 10 }^{ 2 }\)
= 250 + 30 + 100
= 380 cm²
\(\therefore\) P = 150 cm, A = 380 cm²