Question

Calculate the area of a triangle whose sides are 13 cm, 5 cm and 12 cm

Answer 1

Here is the solution :

Given that, Sides of a Triangle are :
5cm , 12cm, 13 cm,

According to Heron's Formula, Area of triangle = √((s)(s-a)(s-b)(s-c))

Where s = Semi perimeter = ((a+b+c)/2)
a,b,c are sides of a Triangle,

Now,

Shortest method for this sum :

We know that are of a Right angle triangle is 1/2 * Base * Height, (B,H not equal to Hypothenuse)

To check if it is a right angled triangle apply Pythagorean formula,

=> 12² + 5² = 13²,
=> 144 + 25 = 169(It's True)

So the triangle formed is right angled,

=> Area = 1/2* 12*5 = 30cm²,

But the correct method :

S =(12+5+13)/2 = 15,
a = 5,
b = 12,
c = 13.

Area = √((15)(10)(3)(2)

=> Area = √(900)(cm⁴)
=> Area = 30cm²,

Therefore area of this triangle is 30cm²,

Hope you understand, Have a Great day !
Thanking you, Bunti 360 !