# What is the area of the triangle which has sides of lengths 9 cm, 3 cm and 7 cm?

hala718 | Certified Educator

We know that the area of the triangle  if given the length of all sides  is:

A = sqrt ( s ( s - a) ( s-b) ( s- c)   where :

s = perimeter / 2

a , b, and c are the sides of the trinagle:

Given the sides are:

a= 3,

b= 7

c = 9

Let us find the perimeter:

p = ( 3 + 7 + 9) = 19\

Then S = p / 2 = 19/ 2 = 9.5

Now let us substitute in the area formula:

A = sqrt[ s ( s- a) ( s-b) ( s-c)]

= sqrt[ 9-5) ( 9.5 - 3) ( 9.5 - 7) ( 9.5 - 9)

= sqrt( 9.5)*6.5*2.5 ( 0.5)

= sqrt(77. 1875)

= 8.79 cm^2( approx,)

Then the area of the triangle is:

A = 8.79 cm^2.

justaguide | Certified Educator

We are given a triangle with sides of length 9 cm, 7 cm and 3 cm.

To find the area we use Heron’s formula which states that for a triangle with sides equal to a, b and c the area is equal to sqrt[ s*(s-a)*(s-b)*(s-c)], where s is the semi perimeter.

Here, the semi perimeter s is equal to (9+7+3)/2 = 19/2 = 9.5. The lengths of the sides are 9, 7 and 3.

Therefore the area = sqrt [ 9.5*(9.5-9)*(9.5-7)*(9.5-3)] = sqrt( 9.5*0.5*2.5*6.5) = sqrt 77.1875 = 8.78 approximately.

Therefore the area of the triangle is 8.78 cm^2.

neela | Student
The three sides of the triangle are 9 cm, 3cm and 7cm. To find thee area of the triangle. We know that if a,b and c are the sides of a triangle then its area is given by: Area = ssqrt{s(s-a)(s-b)(s-c)}, where s = (a+b+c)/2. a = 9cm , b= 3cm and c = 7cm. Therefore s = (9+3+7)/2 = 19/2 = 9.5. Therefore substituting the above values in the formula, we get: Area = sqrt{9.5(9.5-9)(9.5-3)(9.5-7)} Area = sqrt{9.5(0.5)(6.5)(2.5)} Area = sqrt{77.1875 Area = 8.7856 sq cm. Therefore the area of the triangle of the given size is 8.7856sq cm.