Question : The sides of a triangle are 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
Option 1: 20 cm2
Option 2: 28 cm2
Option 3: 24 cm2
Option 4: 16 cm2
Correct Answer: 24 cm 2
Solution :
Given: Sides of the triangle = 6 cm, 8 cm, and 10 cm.
Using Heron's formula the area of a triangle, $A = \sqrt{s(s-a)(s-b)(s-c)}$
Where $s$ is the semi-perimeter of the triangle, which is half the perimeter of the triangle, and $a,b,c$ are the sides of the triangle.
The perimeter of the triangle is the sum of the lengths of its sides, which is:
$P = a + b + c$
Semiperimeter = $s = \frac{a+b+c}{2}$
$s = \frac{6+8+10}{2} = 12$
$A = \sqrt{12(12-6)(12-8)(12-10)}$
$ = \sqrt{12 \times 6 \times 4 \times 2}$
$ = \sqrt{576}$
$ = 24$
Hence, the correct answer is 24 cm
2
.
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