What is the area of the triangle if the sides are 3,5, and 6.

Expert Answers

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

We have the sides of the triangle given as 3, 5 and 6.

We find the area using Heron's formula as

sqrt [ s*(s-a)(s-b)(s-c)]

s = (3 + 5 +6)/2 = 7

sqrt [ s*(s-a)(s-b)(s-c)]

=> sqtr [ 7*(7-3)(7-5)(7-6)]

=> sqrt [7*4*2*1]

=> sqrt 56

The area of the triangle is sqrt 56

Approved by eNotes Editorial
An illustration of the letter 'A' in a speech bubbles

We will use the formula of the area of a triangle given three sides.

The formula is the following:

A = sqrt( s*(s-a)(s-b)(s-c) such that s = perimeter/e , a, b, and c are the sides.

Let us calculate the perimeter.

==> P = 3+5+6 = 14

==> s = 14/2 = 7

==> Now we will substitute into A.

==> A = sqrt( 7*(7-3)*(7-5)*(7-6)

         = sqrt( 7*4*2*1) = sqrt56 = 7.48

Then, the area of the triangle is 7.48 square units.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial