Question

find the area of triangle formed by the points (0,0)(4,0)(4,3) by using heron's formula

Answer 1

Answer:

6 sq. units.  

Step-by-step explanation:

A=(0,0)

B = (4,0)

C = (4,3)

Now find the sides of triangle AB,BC,AC

To find AB use distance formula :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(0,0)$

$(x_2,y_2)=(4,0)$

Substitute the values in the formula :

$AB=\sqrt{(4-0)^2+(0-0)^2}$

$AB=\sqrt{(4)^2}$

$AB=\sqrt{16}$

$AB=4$

To Find BC

$(x_1,y_1)=(4,0)$

$(x_2,y_2)=(4,3)$

Substitute the values in the formula :

$BC=\sqrt{(4-4)^2+(3-0)^2}$

$BC=\sqrt{(0)^2+(3)^2}$

$BC=\sqrt{9}$

$BC=3$

To Find AC

$(x_1,y_1)=(0,0)$

$(x_2,y_2)=(4,3)$

Substitute the values in the formula :

$AC=\sqrt{(4-0)^2+(3-0)^2}$

$AC=\sqrt{(4)^2+(3)^2}$

$AC=\sqrt{16+9}$

$AC=\sqrt{25}$

$AC=5$

So, sides of triangle :

a =4

b=3

c=5

Now to find area:

$Area = \sqrt{s(s-a)(s-b)(s-c)}$  

Where $s = \frac{a+b+c}{2}$  

a,b,c are the side lengths of triangle  

Now substitute the values :  

$s = \frac{4+3+5}{2}$  

$s =6$  

$Area = \sqrt{6(6-4)(6-3)(6-5)}$  

$Area = 6$  

Hence the area of the given triangle is 6 sq. units.