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

Question

1705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-07T06:19:14

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

The side (dimension) given is
#1+sqrt3#

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

So the area of this square
#=(1+sqrt3)^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+2sqrt3 +3#

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