(C) Let the vertices be $A(1, 0)$ and $B(3, 0)$. The length of the side $AB = \sqrt{(3-1)^2 + (0-0)^2} = 2$.The area of an equilateral triangle with s

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(C) Let the vertices be $A(1, 0)$ and $B(3, 0)$. The length of the side $AB = \sqrt{(3-1)^2 + (0-0)^2} = 2$.The area of an equilateral triangle with side length $a$ is given by $\text{Area} = \frac{\sqrt{3}}{4} a^2$.Substituting $a = 2$ into the formula:$\text{Area} = \frac{\sqrt{3}}{4} \times (2)^2 = \frac{\sqrt{3}}{4} \times 4 = \sqrt{3}$.Thus,the area of the triangle is $\sqrt{3}$.

Class 11 Mathematics Straight Line Problems related to triangle and quadrilateral

Medium

If two vertices of an equilateral triangle are $(1, 0)$ and $(3, 0)$,and the third vertex lies in the first quadrant,find the area of the triangle.

A
$\frac{\sqrt{3}}{4}$
B
$\frac{\sqrt{3}}{2}$
C
$\sqrt{3}$
D
$\text{None of these}$

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KVPY 2015

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The area of the parallelogram formed by the lines $a_1x + b_1y + c_1 = 0$,$a_1x + b_1y + d_1 = 0$,$a_2x + b_2y + c_2 = 0$,and $a_2x + b_2y + d_2 = 0$ is:

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If two vertices of an equilateral triangle are $(1, 0)$ and $(3, 0)$,and the third vertex lies in the first quadrant,find the area of the triangle.

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If one of the diagonals of a square is along the line $x = 2y$ and one of its vertices is $(3, 0)$,then the equations of the sides passing through this vertex are:

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