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
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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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