A triangle has sides 3, 4 and 5. Find the area of the triangle using 2 methods

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The area of a triangle with sides 3, 4 and 5 has to be determined using two methods.

It is seen that 3^2 + 4^2 = 9 + 16 = 25 = 5^2

The given triangle is a right-angled triangle. The area of the triangle can be derived using the...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The area of a triangle with sides 3, 4 and 5 has to be determined using two methods.

It is seen that 3^2 + 4^2 = 9 + 16 = 25 = 5^2

The given triangle is a right-angled triangle. The area of the triangle can be derived using the formula A = `(1/2)*b*h`

=> `(1/2)*3*4`

=> 6

Another way to determine the area is to use Heron's formula.

The semi-perimeter of the triangle is `(3 + 4 + 5)/2 = 6`

The area of the triangle is given by `sqrt(6*(6-3)(6-4)(6-5))`

=> `sqrt(6*3*2*1)`

=> `sqrt 36`

=> 6

Using both the methods the area of the triangle with sides 3, 4 and 5 is 6 square units.

Approved by eNotes Editorial Team