Find the area of the triangle if the length of the sides are 3, 8 and 9?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

As we have the length of the sides of the triangle, we can derive the area using the relation

Area = sqrt [s*(s - a)*(s - b)*(s - c)], where s = (a + b + c)/2

a = 3 , b = 8 and c = 9

=> s = 10

Area = sqrt [10*(10 - 3)*(10 - 8)*(10 - 9)]

=> sqrt [10*7*2*1]

=> sqrt 140

The required area of the triangle is sqrt 140.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given a triangle with know 3 sides.

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

==> A = sqrt(s*(s-a)(s-b)(s-c) such that s is the perimeter/2 and a, b, and c are the length of the sides.

Let us calculate the perimeter.

==> p = 3+8+9 = 20

==> s = p/2 = 20/2 = 10

Let us substitute.

==> A = sqrt( 10*(10-3)(10-8)(10-9)

==> A = sqrt( 10*7*2*1) = sqrt140 = 2sqrt35

Then the area of the triangle is 2sqrt35 = 11.83 square units.

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