Find the area of the triangle whose sides are 4, 7, and 9.

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hala718's profile pic

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

Posted on

I am assuming that 4, 7 , and 9 are the length of the sides of the triangle.

We are given the sides of the triangle. Then, we will use the following formula.

Area (A) = sqrt S( S-a) ( S- b) (S-c) such that.

A = area/

S = perimeter / 2

a, b, and c are the sides' length.

let us calculate the perimeter.

We know that the perimeter P = a + b + c

==> P = 4 + 7 + 9 = 20

==> S = 20/2 = 10

==> A = sqrt 10* ( 10 -4) ( 10 - 7) ( 10 -9)

            = sqrt 10*6*3*1

             = sqrt(180) = 6sqrt5 square units.

Then the area of the triangle whose sides 4, 7, and 9 is 6sqrt5 square units.

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The area of a triangle could be determined in 3 ways. When the lengths of the sides are given, Heron's formula is the better choice.

A = sqrt p*(p-a)(p-b)(p-c)

p = (a+b+c)/2 - the half-perimeter of the triangle

We'll put a = 4, b = 7 and c = 9.

p = (4+7+9)/2

p = 20/2

p = 10

A = sqrt 10*(10 - 4)(10 - 7)(10 - 9)

A = sqrt 10*6*3*1

A = 6sqrt 5 square units

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