Q4.    Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Answers (1)

Given the perimeter of the triangle is  42cm and the sides length a= 18cm and b= 10cm

So, a+b+c = 42cm

Or, c = 42 - 18-10 = 14cm

So, the semi perimeter of the triangle will be:

s = \frac{P}{2} = \frac{42cm}{2} = 21cm

Therefore, the area given by the Heron's Formula will be,

A = \sqrt{s(s-a)(s-b)(s-c)}

= \sqrt{21(21-18)(21-10)(21-14)}

= \sqrt{(7\times3 )(3)(11)(7)}

= 21\sqrt{11}\ cm^2

Hence, the area of the triangle is 21\sqrt{11}\ cm^2.

 

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