Question

Find the area of the triangle formed by the points by using Heron's formula.
1) (1, 1), (1, 4) and (5, 1)​

Answer 1

Answer:

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Answer 2

Area of triangle is 6 square units.

Step-by-step explanation:

Consider the given vertices of triangle are A(1, 1), B(1, 4) and C(5, 1)​.

Distance formula:

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

Using distance formula we get

$AB=\sqrt{\left(1-1\right)^2+\left(4-1\right)^2}=3$

$BC=\sqrt{\left(5-1\right)^2+\left(1-4\right)^2}=5$

$AC=\sqrt{\left(5-1\right)^2+\left(1-1\right)^2}=4$

Heron's formula:

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

where, $s=\frac{a+b+c}{2}$ and a,b,c are side lengths.

$s=\frac{3+4+5}{2}=6$

Using Heron's formula we get

$A=\sqrt{6(6-3)(6-4)(6-5)}$

$A=\sqrt{6(3)(2)(1)}$

$A=\sqrt{36}$

$A=6$

Therefore, the area of triangle is 6 square units.

#Learn more

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