Question

find the area of the following traingle formed by the points by usinf using heron's formula 1. (1, 1), (1,4)and (5,1)​

Answer 1

Answer:

Area of the triangle is 6 $unit^2$.

Step-by-step explanation:

The Heron's formula to find the area of the triangle with sides $a, b$ and $c$  is

$Area =\sqrt{s(s-a)(s-b)(s-c)}$

where $s=\dfrac{a+b+c}{2}$

Given the vertices of the triangle are (1,1), (1,4), and (5,1). First, we shall find the length of each side of the triangle. They are nothing but the distance between the vertices. Thus we have

$a=\sqrt{(1-1)^2+(4-1)^2}=\sqrt{3^2}=3\\\\b=\sqrt{(5-1)^2+(1-1)^2}=\sqrt{4^2}=4\\\\c=\sqrt{(5-1)^2+(1-4)^2}=\sqrt{4^2+3^2}=\sqrt{25}=5$

The value of $s$ is $\dfrac{4+3+5}{2}=6$

Hence, the area of the triangle is,

$Area = \sqrt{6(6-4)(6-3)(6-5)}=\sqrt{6\times 2\times 3\times 1}\\\\=\sqrt{36}=6\ unit^2$

Answer 2

QUESTION :

• find the area of the following traingle formed by the points by usinf using heron's formula 1. (1, 1), (1,4)and (5,1)

GIVEN :

• (1, 1), (1,4)and (5,1)

TO FIND :

• find the area of the following traingle = ?

SOLUTION :

S = half of perimeter of traingle B

S = a + b + c /2

area = √ s (s - a) (s - b) ( s - c)

AB = √ ( x 2 - x1 ) +( y2 - y1 ) = √ 9 = 3 = a

BC = √ 16 + 9 = √25 = 5 = b

AC = √ 16 + 0 = √16 = 4 = C

S = 3 + 5 + 4 /2 = 12/2 = 6 = S

A = √ s (s - a) (s - b) ( s - c) = √6(6-3) (6-5) (6-4)

√ 6 .3 . 1 .2 = √36 = 6 sq unit