# What is the area of a square with a dimension of 1+the square root of 3?

Oct 7, 2015

=color(blue)(4+2sqrt3 m^2

#### Explanation:

The side (dimension) given is
$1 + \sqrt{3}$

The formula for area of a square is color(blue)((side)^2

So the area of this square
$= {\left(1 + \sqrt{3}\right)}^{2}$

Here , we apply the identity color(blue)((a+b)^2=a^2+2ab+b^2

So,
(1+sqrt3)^2= 1 +2sqrt3 + (sqrt3)^2

$= 1 + 2 \sqrt{3} + 3$

=color(blue)(4+2sqrt3 m^2 (assuming the unit to be in metre)