Question

Find area of the triangle with vertices at the point given in each of the following:
(1, 0), (6, 0), (4, 3)

Answer 1

Given :

Coordinates of vertices of triangle are:

• (1,0)
• (6,0)
• (4,3)

To Find :

• Area of the triangle

Formula used :

$Area \: of \: triangle =\frac{1}{2} \times |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|$

Solution :

Let us consider the triangle with respective vertices as :

• (1,0) => (x1, y1)
• (6,0) => (x2, y2)
• (4,3) => (x3, y3)

Then,

$Area \: of \: triangle = \frac{1}{2} \times| x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times |1(0 - 3) + 6(3 - 0) + 4(0 - 0) |\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times |- 3 + 18 + 0| \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times| 15| \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 7.5 \: square \: units$

Therefore, area of the triangle is 7.5 square units.