Find the area of triangle whose vertices are 1 1

Asked by admin @ 04/08/2021 in Math viewed by 284 People

Calculate the area of the triangle whose vertices are (1,1) , (2,3) ,(4,5)

Answered by admin @ 04/08/2021

Given:

Vertices = $(1, 1), (2,3), and \ (4,5)$

To prove:

Area of the triangle.

Solution:

Formula:

Area of the triangle = $\frac{1}{2}|[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|\\$

Vertices = $(1, 1), (2,3), and \ (4,5)$

$= x_1= 1\\= y_1= 1\\= x_2=2\\= y_2=3\\= x_3=4\\= y_3=5\\$

$\Rightarrow Area =\frac{1}{2}|[1(3-5)+2(5-1)+4(1-3)]| \\\\\Rightarrow Area =\frac{1}{2}|[1(-2)+2(4)+4(-2)]| \\\\\Rightarrow Area =\frac{1}{2}|[-2+8+-8]| \\\\\Rightarrow Area =\frac{1}{2}|[-2]| \\\\\Rightarrow Area =\frac{1}{2} \times 2 \\\\\Rightarrow Area =\frac{2}{2} \\\\\Rightarrow Area = 1$

The area of triangle is = 1

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