Question

The sides of triangle are 3cm 5cm and 6cm.Then area of triangleis:​

Answer 1

Question

The sides of triangle are 3cm 5cm and 6cm.Then area of triangle is.

Answer

Given:

First side : 3 cm

Second side : 5 cm

Third side : 6 cm

Area of triangle = ??

• See the attachment..

Answer 2

Answer:

Given Information:-

• 1st side of the triangle = 3 cms
• 2nd side of the triangle = 5 cms
• 3rd side of the triangle = 6 cms

To Find:-

Area of the triangle.

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TheAssassin's OBSERVATION:-

Here, the triangle is a Scalene Triangle since sides are different. Heron's formula will work here.

Heron's Fomula:-

√s(s-a)(s-b)(s-c)

where,

1. s = semi perimeter
2. a, b, c = sides of the triangle.

Let's find the semi perimeter!

Semi Perimeter = Perimeter/2

Perimeter = a + b + c

= 3 + 5 + 6 cms

= 14 cms

Therefore, semi perimeter is 7 cms.

Now, finding the area:-

√s(s-a)(s-b)(s-c)

(Heron's Fomula)

= √7(7-3)(7-5)(7-6) cm²

(Written as per the formula)

= √7(4)(2) cm²

(Subtraction can be seen / simplified)

= √7 (2)(2)(2) cm²

(Extended 4 by prime factorisation)

= 2√7(2) cm²

(2 is taken out)

= 2√14 cm²

(Solution)

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•°• Area of the triangle is 2√14 cm².