Question

Area of the triangle with vertices (1,1),(2,1) and (1,2) is
a) sq.un
unit b) sq.unit c) 1sq.unit
d) 2sq.unit​

Answer 1

Answer:

Area of the triangle is 0.5 units²

Explanation:

Given vertices of the triangle are :-

• (1, 1)
• (2, 1)
• (1, 2)

Area of the triangle is given by :-

${ \longrightarrow \: \rm \dfrac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| }$

Where,

• $\rm x_1, x_2, \& x_3 \: are \: 1, 2, \: and \: 1 \: respectively$
• $\rm y_1, y_2, \& y_3 \: are \: 1, 1, \: and \: 2 \: respectively$

Substituting the given coordinates :-

${ \longrightarrow \: \rm \dfrac{1}{2}|1(1 - 2) + 2(2 - 1) + 1(1 - 1)| }$

${ \longrightarrow \: \rm \dfrac{1}{2}|1( - 1) + 2(1) + 1(0)| }$

${ \longrightarrow \: \rm \dfrac{1}{2}| - 1 + 2 + 0| }$

${ \longrightarrow \: \rm \dfrac{1}{2}|1| }$

${ \longrightarrow \: \rm \dfrac{1}{2} }$

${ \longrightarrow \rm \: 0.5 \: {units}^{2} }$

∴ Area of the triangle is 0.5 units²

__________________________

Formula used :

${ \longrightarrow \: \bf \dfrac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| }$

Where,

• $\bf x_1 \& y_1$ denotes the coordinates of first point.
• $\bf x_2 \& y_2$ denotes the coordinates of second point.
• And $\bf x_3 \& y_3$ denotes the coordinates of third point.