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Question

The area of a triagnle with sides 3cm , 5 cn, 6 cm is-

28 c m^{2}

2 \sqrt{14} c m^{2}

3 \sqrt{14} c m^{2}

\sqrt{14} c m^{2}

ANSWER : 2

Descrption

To find the area of a triangle with sides of length 3 cm, 5 cm, and 6 cm, you can use Heron's formula. Heron's formula states that the area (A) of a triangle with sides of length a, b, and c is given by:A = √[s(s - a)(s - b)(s - c)]Where s is the semiperimeter of the triangle, calculated as:s = (a + b + c) / 2In this case, the sides of the triangle are a = 3 cm, b = 5 cm, and c = 6 cm. Let's calculate the semiperimeter first:s = (3 + 5 + 6) / 2 = 14 / 2 = 7 cmNow, we can use Heron's formula to find the area:A = √[7(7 - 3)(7 - 5)(7 - 6)]A = √[7(4)(2)(1)]A = √[7 * 4 * 2]A = √[56]Now, simplify the square root:A = √[4 * 14]A = 2√14So, the area of the triangle with sides 3 cm, 5 cm, and 6 cm is 2√14 square centimeters.

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