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Today we are going to talk about some important arithmetic formulae on triangle. we are giving whole complete list of all the formulae here ,which are very helpful to solve the problems quickly and accurately. Triangle is a very important topic of mensuration , so it is advised to students that they learn these formulae and keep practicing with it.

**SOME IMPORTANT SUTRAS**

1). Area of triangle = (b×h)/2

2). Perimeter of the triangle = a+b+c

3). Semi-perimetre of the triangle = (a+b+c)/2

4). Area of right angled triangle = bp/2

5). Area of triangle = pbsinθ/2

6). Area of triangle = (area of rectangle or parallelogram)/2

7). Height of triangle = 2A/b

8). Area of isoceles right angled triangle = (hypotenuse)^2/4

9). Area of isoceles right angled triangle =

(equal side)^2/2

10). Hypotenuse of isoceles right angled triangle = 2√Area

11). Hypotenuse of isoceles right angled triangle= side√2

12). Equal side of isoceles right angled triangle = area√2

13). Equal side of isoceles right angled triangle= hypotenuse/√2

14). If the two equal side of isoceles triangle is a and other side is b , then area of triangle =

(b/4)√(4a^2-b^2)

15). Area of isoceles triangle = a^2.sinθ/2

16). Area of triangle = √s(s-a)(s-b)(s-c) , where s = (a+b+c)/2

17). Area of isoceles triangle = √s(s-a)^2.(s-b)

18). Area of equilateral triangle = (√3/4).a^2

19). Height of equilateral triangle = (√3/2).a

20). Side of equilateral triangle = 2√(A/3)

21). Perimeter of equilateral triangle = 3×side

22). Side of equilateral triangle= 2h/√3

23). If x is increased or decreased in the side a of equilateral triangle , then difference in area =

(√3/4)(x^2+-2ax)

24). If x times is increased or decreased in the side a of equilateral triangle , then difference in area = (√3/4)(x^2+-1)

25). Radius of circle which is inside the equilateral triangle = a/2√3

26). Radius of circle , when a equilateral triangle is in the circle= a/√3

27). Radius of circle inside the triangle ABC is =

√s(s-a)(s-b)(s-c)/s

28). Radius of circle which is inside the right angled triangle = (area of right angled triangle/s)

* [Where s is semi-perimetre]

29). Radius of the circle, which is outside of the equilateral triangle of altitude h.= 2h/3

30). When the midpoint of the two side is the equilateral triangle of side a is joined, then the area of the small triangle formed by doing so is = (√3/16).a^2

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