Area of Triangle With Two Sides and Included Angle (SAS)
Formula for the Area Of SAS Triangle is obtained by using the concept of trigonometry.
Let us assume ABC is right angled triangle and AD is perpendicular to BC.
In the above figure,
Sin B = AD/AB
⇒ AD = AB Sin B = c Sin B
⇒ Area of Triangle ABC = 1/2 ⨯ Base ⨯ Height
⇒ Area of Triangle ABC = 1/2 ⨯ BC ⨯ AD
⇒ Area of Triangle ABC = 1/2 ⨯ a ⨯ c Sin B
= 1/2 ⨯ BC ⨯ AD
Thus,
Area of Triangle = 1/2 ac Sin B
Similarly, we can find that ,
Area of Triangle = 1/2 bc Sin A
Area of Triangle = 1/2 ab Sin C
We conclude that the area of triangle using trigonometry is given as the half the product of two sides and sine of the included angle.
Area of Triangle | Formula and Examples
Area of a triangle is the region enclosed by all its three sides. It is generally calculated with the help of its base and height. To Find the Area of a triangle A with base b and height h, We use the formula, A = [Tex]\frac{1}{2} \times b \times h [/Tex].
Let’s learn about the area formulas for different types of triangles in detail, with the help of solved examples.
Table of Content
- What is the Area of the Triangle?
- Area of Triangle Formula
- Area of Right Angled Triangle
- Area of Equilateral Triangle
- Area of Isosceles Triangle
- Area of Triangle By Heron’s Formula
- Area of Triangle With Two Sides and Included Angle (SAS)
- Area of Triangle in Coordinate Geometry
- Solved Examples on Area of Triangle
- Practice Problems on Area of Triangle