पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

88 DETERMINATIONS
the truth ; as for example, in the case of the triangle having 13
for the two (flank) sides and 24 for the base, the gross area is
156, whereas the correct area is 60.
I shall therefore state the methods for obtaining the
accurate results only.
(ii) AREA OF THE QUADRILATERAL WITH EQUAL
ALTITUDES AND OF THE TRIANGLE
Rule for finding the area of a quadrilateral in which the per-
pendiculars dropped from the vertices to the base are equal,
and that of a triangle :
115. In the case of a quadrilateral, in which the per-
pendiculars dropped from the vertices to the base are equal,
and a triangle, half the sum of the base and the face, multi-
plied by the altitude, gives the area.¹
That is,
(i) area of a quadrilateral with parallel base and face
base + face
= ——————————— × altitude;
2
(ii) area of a triangle = ½ base × altitude.
Ex. 122. In an equilateral quadrilateral, the face, the
base, and the altitude are all equal to the flank sides, each
being 1½ cubits in length. Say, friend, what is the area of
that (quadrilateral).
Ex. 123. Give out the area of that rectangular quadri-
lateral in which the base and face are each 5½ cubits, and the
flank sides and altitude each 3 cubits.
Ex. 124. In a triangle the (flank) sides are 4 - ¼ and
3¼ cubits, the base is 3½ cubits, and the altitude is 3 cubits.
What is the area of that ?
Ex. 125. In an equilateral triangle the base is 8½ cubits,
and the altitude is 7 cubits and 8⅔ aṅgulas. What is the area
thereof ?
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¹ The same rule is given in MSi, xv. 78; SiŚe, xiii. 30; L(ASS), p. 162,
line 3; GK, II, p. 42, lines 10-11; and page 50, lines 13-14.