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

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The area of a triangle is given by sqrt [ s(s - a)(s - b)(s - c)] where s is the semi-perimeter and a, b and c are the lengths of the sides.

Substituting the lengths of the sides as 4, 7 and 9, the value of s = 10

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

=> sqrt [ 10(10 - 4)(10 - 7)(10 - 9)]

=>sqrt (10*6*3*1)

=> sqrt 180

=> 6*sqrt 5

**The area of the triangle is 6*sqrt 5**

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**