Q12 of 14 Page 206

The semi-perimeter of the triangle is 132cm and the product of the difference of semi-perimeter and its respective sides are 13200 cm (square). Find the area of a triangle.

Let the sides of the triangle be a, b and c.


Given that Semi-perimeter = s = 132cm.


Also, a product of the difference of semi-perimeter and its respective sides are 13200 cm2.


i.e. s(s – a)(s – b)(s – c) = 13200


∴ we know by Heron’s formula.


Area of a triangle with sides a, b, c, and semi-perimeter s is given by


=


Substituting s and in above equthe ation we get


=


= 1320 cm2


∴ The area of a triangle is 1320cm2.


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