# Show that the Points O(0,0), A( 3,Sqrt(3)) and B (3,-sqrt(3)) Are the Vertices of an Equilateral Triangle. Find the Area of this Triangle. - Mathematics

Show that the points O(0,0), A( 3,sqrt(3)) and B (3,-sqrt(3)) are the vertices of an equilateral triangle. Find the area of this triangle.

#### Solution

The given points are O(0,0), A( 3,sqrt(3)) and B (3,-sqrt(3)) .

OA = sqrt((3-0)^2 +{ (sqrt(3)) -0}^2) = sqrt((3)^2 +(sqrt(3))^2) = sqrt(9+3) = sqrt(12) = 2sqrt(3) units

AB = sqrt((3-3)^2 +(-sqrt(3)-sqrt(3))^2) = sqrt((0) + (2 sqrt(3))^2) = sqrt(4(3)) = sqrt(12) =2sqrt(3) units

OB = sqrt((3-0)^2 + (-sqrt(3) -0)^2) = sqrt((3)^2 +(sqrt(3)^2) = sqrt(9+3) = sqrt(12) = 2 sqrt(3) units

Therefore, OA =AB = OB = 2 sqrt(3)   units

Thus, the points O(0,0), A( 3,sqrt(3)) and B (3,-sqrt(3))  are the vertices of an equilateral triangle Also, the area of the triangle OAB = sqrt(3)/4 xx (" side")^2

=sqrt(3)/4 xx(2 sqrt(3) )^2

= sqrt(3)/4 xx 12

= 3 sqrt(3)    square units

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 25