How many tiles, each of area 400 cm², will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide ?

Given:

Dimensions of grass plot (ABCD) = 25 x 13 m

Width of footpath = 2 m

Area of footpath = Area of ABQP + Area of QNOR + Area of RCDS + Area of SHMP

= 2Area of ABQP + 2Area of QNOR

= 2(Area of ABQP + Area of QNOR)

Area of ABQP = l x b = AB x AP

= 25 x 2 m²

= 50 m²

Area of QNOR = l x b = DN x QN

= 17 x 2 m²

= 34 m²

Area of footpath = 2(50 + 34) m²

= 2 x 84 m²

= 168 m²

= 1680000 sq. cm

Total area = Number of tiles x Area covered by 1 tiles

⇒ 1680000 = Number of tiles x 400

⇒ Number of tiles = $\dfrac{1680000}{400}$

= 4200

Hence, the number of tiles = 4200.