Given the triangle $ABC$. If length of medians $AM=7.5$ and $BN=12$ and side $AC=6$, find the area of the triangle.
NOTE: Solution must not use any special formula or trigonometric functions.
My attempt : $NM$ is half of $AB$ in length, Triangles $ANO$ and $MOB$ have same amount of area.
Best Answer
First, use the lengths to solve for the semiperimeter ( which is half the perimeter ). Then set up Heron's formula (which would be area is equal to the square root of semiperimeter multiplied by semiperimeter minus side a multiplied by semiperimenter minus side b multiplied by semiperimenter minus side c. Here are the formulas you need:
S(semiperimeter)= 1/2 (a+b+c)
A (area)=√S (S-a)(S-b)(S-c)