Homework Help

Calculate the area of a triangle if it has length of legs as 6cmm, 8cm and 10cm.

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christiano-cr7 | (Level 1) Salutatorian

Posted July 4, 2013 at 10:03 AM via web

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Calculate the area of a triangle if it has length of legs as 6cmm, 8cm and 10cm.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 4, 2013 at 10:14 AM (Answer #1)

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Here we must look at the length closely. We can find that they are combined in the following manner.

`6^2+8^2 = 10^2`

This means the triangle is a right triangle.

The area of the right triangle is given by;

A = 1/2(product of leg length except hypotenuse)

 

So the area of the triangle can be given as;

`A = 1/2xx6xx8`

`A = 24cm^2`

 

So the area of the triangle given is `24cm^2` .

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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted July 4, 2013 at 11:20 AM (Answer #2)

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Since the length of the three sides of the triangle are given, to determine its area, apply Heron's formula.

`A=sqrt(s(s-a)(s-b)(s-c))`

where a, b and c are the sides of the triangle, and s is half of its perimeter.

So,

`s=(a+b+c)/2=(6+8+10)/2=24/2=12`

`A=sqrt(12(12-6)(12-8)(12-10))=sqrt(12*6*4*2)` 

`A=sqrt576=24`

Hence, the area of the triangle is `24 cm^2` .

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