# Mensuration part 10

Problem 1: A rectangular park whose length and breadth are 30m and 20m, is surrounded by 2m broad road. Find the area of the road ?

Solution:

Area =(l+b+2w)2w

(30+20+4)*4)=216

Problem 2: A rectangular field whose sides are 50m × 40m has two straight road of width 2m and connects their opposite sides. Find the area of the road?

Solution:

Area of shaded region = (50+40-2)*2 = 88*2 =176

Problem 3: The area of a rectangle whose one side is ‘a’ is ‘2a2’. What is the area of a square having one of the diagonals of the rectangle as side?

Solution:

$2a^{2}=a\times&space;b$

$b=2a$

Diagonal =$\sqrt{a^{2}+4a^{2}}=\sqrt{5a^{2}}$

Area of a square = $(\sqrt{5a^{2}})^{2}=5a^{2}$