Activity › Discussion › Math › Heron’s Formula
Tagged: Heron's Formula

Heron’s Formula
Posted by Prateek on February 2, 2024 at 4:27 pmFind the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.
brajesh replied 5 months, 2 weeks ago 2 Members · 1 Reply 
1 Reply

::
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 semiperimeter (s) as follows:
A = âˆš(s(sa)(sb)(sc))
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 cmNow 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(2118)(2110)(2114))
= âˆš(21(3)(11)(7))
= âˆš(21311*7)
= âˆš(5397)
â‰ˆ 73.49 cmÂ²Therefore, the area of the triangle is approximately 73.49 square centimeters.