Question

Using Heron's formula, find the area of a triangle whose sides are 6 cm, 8 cm and 10 cm.


Step by step explaination

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Answer 1

24 cm2

Step-by-step explanation:

Using the formulas

A=√s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c/2

Solving forA=14﹣a4+2(ab)2+2(ac)2b4+2(bc)2c4

=1﹣64+2·(6·8)2+2·(6·10)2﹣84+2·(8·10)2﹣104

=24cm²

Answer 2

$a=6cm\\b=8cm\\c=10cm\\\\s=\frac{a+b+c}{2}$

$s=\frac{6+8+10}{2}\\\\s=12cm$

$Area=\sqrt{s(s-a)(s-b)(s-c)}\\ \\=\sqrt{12(12-6)(12-8)(12-10)}\\\\=\sqrt{12(6)(4)(2)}\\\\=\sqrt{12(48)}\\\\=\sqrt{576}\\\\ =24cm^2$