Question

find the area of the triangle whose vertices are (2,2),(5,2),(2,6)​

Answer 1

ANSWER:

Given:

• Vertices of triangle = (2,2), (5,2), (2,6)

To Find:

• Area of triangle.

Solution:

We are given that, the vertices of triangle have coordinates, = (2,2), (5,2), (2,6).

We know that,

$\hookrightarrow\text{Area of Triangle}=\dfrac{1}{2}\bigg|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigg|$

In this question,

• x₁ = 2
• x₂ = 5
• x₃ = 2
• y₁ = 2
• y₂ = 2
• y₃ = 6

So,

$\implies\text{Area of the Triangle}=\dfrac{1}{2}\bigg|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigg|$

$\implies\text{Area of the Triangle}=\dfrac{1}{2}\bigg|2(2-6)+5(6-2)+2(2-2)\bigg|$

So,

$\implies\text{Area of the Triangle}=\dfrac{1}{2}\bigg|2(-4)+5(4)+2(0)\bigg|$

$\implies\text{Area of the Triangle}=\dfrac{1}{2}\bigg|-8+20+0\bigg|$

$\implies\text{Area of the Triangle}=\dfrac{1}{2}\bigg|12\bigg|$

$\implies\text{Area of the Triangle}=\dfrac{1}{2\!\!\!/}\times12\!\!\!\!/^{\:6}$

Hence,

$\implies\text{\bf Area of the Triangle = 6square units}$

Therefore, the area of the Triangle with vertices (2,2), (5,2), (2,6) is 6sq. units.