Knowing how to calculate the area of a triangle is a fundamental skill in geometry and math. There are several formulas that can be used to calculate the Area triangle (oppervlakte driehoek), depending on the information you have available. In this article, we’ll discuss four different formulas for calculating the area of a triangle, along with some helpful examples.
The Heron Formula
The Heron formula is used when all three sides of a triangle are known. This formula is named after the Greek mathematician Hero of Alexandria and is also known as Hero’s formula. The Heron formula is expressed as A = √s (s-a)(s-b)(s-c), where A represents the area, s is half of the perimeter (or semiperimeter) of the triangle, and a, b, and c represent each side length. For example, if you have a triangle with side lengths 3, 4 and 5 cm, then you would use this formula as follows: A = √(6) (6 – 3)(6 – 4)(6 – 5) = 6√3 cm2.
The Sine Law Formula
The Sine Law formula can be used when two sides and one angle opposite one of those sides are known (such as when two angles and one side length are given). It states that A/sinA = b/sinB = c/sinC, where A represents one angle (in degrees) while b and c represent corresponding side lengths. For example, if you have an angle A measuring 40° and side lengths b measuring 10 cm and c measuring 8 cm., then you would use this formula as follows: A/40 = 10/x = 8/y; solving for x yields 30° for B and y yields 56° for C. Finally, using sinA x sinB x sinC gives us 0.48 cm2 for the area.
The Cosine Law Formula
The Cosine Law formula can be used when all three sides of a triangle are known but none of its angles are given (such as when only three side lengths are given). It states that c2=a2+b2−2abcosC ,where C represents one angle while a and b represent corresponding side lengths. To find the area using this formula first solve for C in terms of cosC by rearranging terms so that it reads cosC=(a2+b2−c2)/(2ab). Then plug those values into the Heron formula mentioned above to get your answer! For example, if we have side lengths 3 cm., 4 cm., and 5 cm., then we would solve this equation as follows: cosC=(32+42−52)/(24) = 0.5; from there we get C = 60° which allows us to use this value in our Heron equation above to get 6√3=10.82762530298219…cm2 for our answer!
Knowing how to calculate the area of a triangle correctly can help you immensely in mathematics or any other field requiring geometric calculations such as architecture or engineering. In this article, we discussed four different formulas for calculating the area of a triangle depending on what information is available—the Heron Formula (when all three sides are known), Sine Law Formula (when two sides & one angle opposite one side are known), Cosine Law Formula (when only three side lengths are given).
