Question

Find the area of A traingle whose sides are 6cm, 8cm, 12cm respectively.​

Answer 1

Question:

Find the area of triangle whose sides are 6cm, 8cm, 12cm respectively.

Answer:

21.330cm

Step-by-step explanation:

Given the area of triangle

Let a = 6cm

Let b = 8cm

Let c = 12cm

We are going to use Herons Formula

Heron's Formula used in the sum: $s=\frac{a+b+c}{2} , \sqrt{s(s-a)(s-b)(s-c)}$

Let us apply in the first formula that is $s=\frac{a+b+c}{2}$

⇒ $s=\frac{6+8+12}{2}$

⇒ $s=\frac{26}{2}$

⇒ $s=13$

Hence the semi perimeter is 13 cm

Now let us apply in Heron's formula

⇒$\sqrt{s(s-a)(s-b)(s-c)}$

⇒$\sqrt{13(13-6)(13-8)(13-12)}$

⇒$\sqrt{13(7)(5)(1)}$

⇒$\sqrt{13(35)}$

⇒$\sqrt{455}$

⇒21.330cm

Hence your answer is 21.330

Answer 2

The required area of the triangle is  $21.330$$cm^{2}$.

Heron's Formula

The semi perimeter and area of the triangle are given by relations.

$s=\frac{a+b+c}{2}, \sqrt{s(s-a)(s-b)(s-c)}$

where,

s is the semi perimeter of the triangle,

a, b, c are the three sides of the triangle.

Given:

side  $a=6 \mathrm{~cm}$

side  $b=8 \mathrm{~cm}$

side  $c=12 \mathrm{~cm}$

Explanation:

Calculate the semi perimeter as given below,

$s=\frac{a+b+c}{2}$

$\begin{aligned}&\Rightarrow s=\frac{6+8+12}{2} \\&\Rightarrow s=\frac{26}{2} \\&\Rightarrow s=13\end{aligned}$

Hence the semi perimeter is $13 \mathrm{~cm}$.

Now let us apply in Heron's formula to get the area,

$\begin{aligned}&\Rightarrow \sqrt{s(s-a)(s-b)(s-c)} \\&\Rightarrow \sqrt{13(13-6)(13-8)(13-12)} \\&\Rightarrow \sqrt{13(7)(5)(1)} \\&\Rightarrow \sqrt{13(35)} \\&\Rightarrow \sqrt{455} \\&=21.330 \mathrm{~cm^{2} }\end{aligned}$

Therefore, the required area is  $21.330$$cm^{2}$.

To know more about triangle and its types, here

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