Lesson Formulas for area of a triangle

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Formulas for area of a triangle


1.  S = a%2Ah%2F2.

     The area of a triangle equals half the product of the measure of any its side  (a)  and the measure of the altitude drawn to this side  (h).


2.  S = a%2Ab%2Asin%28gamma%29%2F2.

     The area of a triangle equals half the product of the measures of any two its sides  (a  and  b)  and the sines of the angle included by these sides.


3.  S = r%2Ap.

     The area of a triangle equals the product of its semi-perimeter  p  and the radius of the inscribed circle  r.


4.  S = sqrt%28p%28p-a%29%28p-b%29%28p-c%29%29 = .

     It is the Heron's formula named after the ancient Greek mathematician Heron.
     Here a,  b  and  c  are the measures of a triangle sides and  p  is half the perimeter:  p = %28a+%2B+b+%2B+c%29%2F2.

5.  S = abc%2F4R.

     Here a,  b  and  c  are the measures of a triangle sides and  R  is the radius of the circumscribed circle.

Right-angled triangle


6.  S = a%2Ab%2F2.

     The area of a right-angled triangle equals half the product of the measures of its legs  a  and  b.

Equilateral (or regular) triangle


7.  S = a%5E2%2Asqrt%283%29%2F4.

     The area of a regular triangle equals the square of its side  a  multiplied by sqrt%283%29%2F4 .


My other lessons on the topic  Area  in this site are
    - WHAT IS area?
    - Proof of the Heron's formula for the area of a triangle
    - One more proof of the Heron's formula for the area of a triangle
    - Proof of the formula for the area of a triangle via the radius of the inscribed circle
    - Proof of the formula for the radius of the circumscribed circle
    - Area of a parallelogram
    - Area of a trapezoid
    - Area of a quadrilateral
    - Area of a quadrilateral circumscribed about a circle  and
    - Area of a quadrilateral inscribed in a circle
under the topic  Area and surface area  of the section  Geometry,  and
    - Solved problems on area of triangles
    - Solved problems on area of right-angled triangles
    - Solved problems on area of regular triangles
    - Solved problems on the radius of inscribed circles and semicircles
    - Solved problems on the radius of a circumscribed circle
    - A Math circle level problem on area of a triangle
    - Solved problems on area of parallelograms
    - Solved problems on area of rhombis, rectangles and squares
    - Solved problems on area of trapezoids  and
    - Solved problems on area of quadrilaterals
under the topic  Geometry  of the section  Word problems.

For navigation over the lessons on  Area of Triangles  use this file/link  OVERVIEW of lessons on area of triangles.

To navigate over all topics/lessons of the Online Geometry Textbook use this file/link  GEOMETRY - YOUR ONLINE TEXTBOOK.

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