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Let the triangle be triangle ABC
AND D be the midpoint of side BC
AND side AE be the perpendicular from point A to side BC such that
A(triangle ADB)/A(triangle ADC) = (1/2 * AD * DB) / (1/2 * AD * DC)
AS area of a triangle is equal to half the product of its base and height
hence A(triangle ADB)/A(triangle ADC) = DB/BC
= (1/2 * BC) / (1/2 * BC)
AS point D is midpoint of side BC
hence A(triangle ADB)/A(triangle ADC) = 1
hence A(triangle ADB) = A(triangle ADC)
hence we can say that a median of a triangle divides it into two triangles of equal area.

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