Saturday, December 10, 2011

Plane Geometry Review : Triangle Area calculation

Area Formulas

1.  Given base and altitude
Area triangle given base and height
Triangle: Given base and height
Area = 1/2 (b)(h)

2. Given two sides and an Angle

area of triangle given 2 sides and an angle
 Triangle:  Given 2 sides and angle
Area = 1/2 (a) (b)sin θ

3. Given 3 sides
Area of triangle given 3 sides
Triangle Given 3 sides a,b,c

Area = sqrt (s(s-a)(s-b)(s-c))----->  Heron's Formula  
where s= (a+b+c)/2

4. Triangle inscribed in a circle
area of Triangle inscribed in a cirle
r= radius of the circle 
Area = (a b c)/ 4r

5. Given a circle inscribed in a Triangle

area of a triangle in a circle inscribing it
r = radius of the circle

Area  =  rs 
s = ( a+b+c/) 2

6. Circle escribed by the triangle

area of triangle given a circle escribing it
where a is the side tangent to the circle
Area =  r (s-a)
s = ( a+b+c/) 2

Friday, December 9, 2011

Engineering Mathematics : Plane Geometry Part 1

Fundamental Principles


  • Acute angle = less 90 deg
  • Obtuse angle = more than 90 and less than 180 deg
  • Straight angle =180 deg
  • Vertex of the angle is point where two lines meet
  • Supplementary angles have a sum of 180 deg
  • Complementary angles have a sum of 90 deg
  • The base angles of an isosceles (two equal sides) triangle =  60 deg
  • Each angle of an isosceles right triangle = 45 deg
  • Exterior angle of a triangle is the sum of the remote interior angle
  • The sum of the angles of a polygon of n sides = (n-2)180 deg
  • The sum of the exterior angles of any polygon = 360 deg

Congruence of triangle
In geometry,Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size

conditions:   (s=side  ; a=angle)
  • s.a.s =s.a.s   (Side-Angle-Side)
  • a.s.a=a.s.a  (Angle-Side-Angle)
  • s.s.s=s.s.s  (Side-Side-Side
  • a.a.s=a.a.s (Angle-Angle-Side)

conguent triangle condition

Two right triangles are congruent if hypotenuse and leg of one hypotenuse and corresponding leg of the other.