💯 Maths

# How do I find the area of a triangle when I only know the three side lengths?  Verified
Zhen HuaExperienced GCSE Maths&Biology Tutor88 students helped

There are two methods to find the area: Method 1: use cosine rule to find out one angle: cosA=(b^2+c^2-a^2)/2bc, and then use area formula 1/2bcSinA to work out the area. Method 2: use Heron's formula which is Area=(s(s-a)(s-b)(s-c))^1/2, where s=(a+b+c)/2, but neither A-level nor GCSE will use Heron's formula to solve area for triangle, and I believe Heron's formula is not in mark scheme, so you don't need to learn the second method. The first method is more common. I hope you find this answer helpful. By Herons formula , you can find the area of the triangle  Verified
Renat SamurResourceful tutor and who is ready to teach!82 students helped

Let’s say we have a triangle with lengths a, b and c. Now we gotta find an angle so we can use the equation: Area=1/2 * (length of side 1) * (length of side 2) * sin(the angle opposite side 3) To do this we use the cosine rule which states: a^2 + b^2 -2ab*cosC=c^2 Where C is the angle opposite the side length c. Now we rearrange: cosC = (a^2 + b^2 - c^2)/(2ab) Solving for C we can now use: Area = 1/2 ab*cosC Nigel RimandoData Professional by trade. Teacher at heart.10 students helped

Hi, the most straightforward answer to this inquiry would be by using Heron's formula which is: Area = sqrt( p ( p - a ) ( p - b ) ( p -c ) ) where a, b, and c are the lengths of the sides of the triangle, and p is 1/2 of the perimeter (i.e. (a + b + c) / 2). This formula works for any type of triangle, as long as a, b, and c are actually valid lengths to form a triangle. Another way involving trigonometry is to use the cosine law, but that will involve having to calculate the angles for the triangle.  Verified
faizah Begumhelping you get the grades you deserve!231 students helped

use the cosine rule b^2 + C^2 -A^2/ 2bc to find the cosA angle. then do cos-1 to find the angle. then use sine rule= 1/2AB sinC to find the area Hope it works  Verified 