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Activity Discussion Math Heron’s Formula

• Heron’s Formula

Posted by on February 2, 2024 at 4:27 pm

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

replied 6 days, 11 hours ago 2 Members · 1 Reply
• brajesh

Member
February 24, 2024 at 10:46 am
0

To find the area of a triangle when two sides and the perimeter are known, we can use Heron’s formula. Heron’s formula states that the area (A) of a triangle with sides a, b, and c can be calculated using the semi-perimeter (s) as follows:

A = âˆš(s(s-a)(s-b)(s-c))

where s = (a + b + c) / 2.

In this case, the two sides given are 18 cm and 10 cm, and the perimeter is 42 cm. Let’s calculate the area:

s = (a + b + c) / 2 = (18 + 10 + c) / 2 = (28 + c) / 2 = 14 + c/2

Since the perimeter is 42 cm, we have:

42 = 18 + 10 + c
42 = 28 + c
c = 42 – 28
c = 14 cm

Now we can substitute the values of a, b, and c into Heron’s formula:

s = (18 + 10 + 14) / 2 = 42 / 2 = 21

A = âˆš(21(21-18)(21-10)(21-14))
= âˆš(21(3)(11)(7))
= âˆš(21311*7)
= âˆš(5397)
â‰ˆ 73.49 cmÂ²

Therefore, the area of the triangle is approximately 73.49 square centimeters.

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