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198
GANITASĀRASANGRAHA.
The rule for arriving at the minutely socurate measurement of the area (of trilateral and quadrilateral figures) -
50. Four quantities represented (respectively). by balf the sum of the sides as diminished by (each of) the sides (taken in order) are multiplied together; and the square root (of the produot so obtained) gives the minutely accurate measure (of the area of the figure). Or the measure of the areas may be arrived at by multiplying by the perpendicular (from the top to the base) half the sam of the top measure and the base measure. (The lattor rule does not hold good) in the case of an inequi-lateral quadrilateral figure.
Examples in illustration thereof. 51. In the case of an equilateral triangle, 8 dandas give the measure of the base is also of each of the two sides. You, who know caloulation, tell me the accurate value of the area (thereof) and also of the perpendicular (to the base) as well as of the segments (of the base caused thereby).
52. In the case of an isosceles triangle (ouch of the) two (equal) sides measures 13 dandax, and the base measures 10. (What is) the accurate measure of the area thereof, and of the perpendi
50. Algebraioally represented :
Aron of a trilateral figure = V (-a) (A-6) (a-c); where # is half the sum of the sides, a, b, c, the respective measures of the sides of the trilatorul figaro;
P, whero p is the perpendioclar distance of the vertex from the baso.
Aroa of a quudrilateral figure = V TR-a) (8-6) (0-c) (-d) where is half the sum of the vides, and a, b, c, d the measures of the respootive sides of the quadrilateral figure ;
* p (except in the 0.40 of an inequilateral quadrilateral) where is the measure of either of the porpendicolars drawn to the base from the extremi.
ties of the top aide. The formulas here given for trilateral figures are oorroot; but those given for quadrilatral figures hold good only in the case of oy olio quadrilaterals, as in these formulas vight is loat of the faot that for the same messore of the sides the value of the area as well as of the perpendioular may vary.
or =
0+d
