Question

Q.1) Find the area of the triangle whose sides are 13cm,14cm,15cm.


Need a correct answer

Answer 1

The following Question is a part of Application of Heron's Formula

Your Answer:

Given:-

$\tt \star a = 13cm \\\\ \tt \ \star b = 14cm \\\\ \tt \star c = 15cm \\\\ \tt Where \ \ a,b \ \ and \ \ c \ \ are sides \ \ of \ \ the \ \ Triangle$

Solution:-

We know that

$\tt Area \ \ of \ \ Triangle =\sqrt{s(s-a)(s-b)(s-c)} \\\\ \tt Where \ \ s \ \ is \ \ the \ \ semi-perimeter \ \ of \ \ Triangle$

So, finding 's' first

$\tt s = \dfrac{a+b+c}{2} \\\\ \tt \Rightarrow s = \dfrac{13+14+15}{2} \\\\ \tt \Rightarrow s = \dfrac{42}{2} \\\\ \tt \Rightarrow s= 21$

Now replacing values of s,a,b and c

$\tt Area = \sqrt{21(21-13)(21-14)(21-15)} \\\\ \tt \Rightarrow Area = \sqrt{21 \times 8 \times 7 \times 6} \\\\ \tt \Rightarrow Area = \sqrt{7\times 3 \times 4 \times 2 \times 7 \times 3 \times 2} \\\\ \tt \Rightarrow Area = 7 \times 3 \times 2 \times 2 \\\\ \tt \Rightarrow Area = 21 \times 4 \\\\ \tt \Rightarrow Area = 84cm^2$

Sp, the area of triangle is  84cm^2

Answer 2

Question:-

➣ Find the area of the triangle whose sides are 13cm,14cm,15cm.

AnSwER:-

➣

Given:-

➣a = 13cm

➣ b = 14cm

➣ c = 15cm

Here, a , b and c are sides of the Triangle.

Solution:-

We know:-

Heron's Formula:-

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

•Finding Semi Perimeter(s):-

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

s = $\dfrac{13+14+15}{2}$

s = $\dfrac{42}{2}$

s = $\cancel{\dfrac{42}{2}}$

s= 21

• Replacing values of s,a,b and c:-

➣Area = $\sqrt{21(21-13)(21-14)(21-15)}$

➣Area = $\sqrt{21 \times 8 \times 7 \times 6}$

➣Area = $\sqrt{7\times 3 \times 4 \times 2 \times 7 \times 3 \times 2}$

➣Area = $7 \times 3 \times 2 \times 2$

➣Area = $21 \times 4$

➣Area = $84cm^2$

Therefore, the Area of Triangle is : 84cm²