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194 mensuration.
Example.
Find the area of a triangle 16 inches long and 5 inches per-
pendicular height.
Solution
:
Area = - = 40 square inches.
The perpendicular height in any triangle is equal to the
area multiplied by 2 and the product divided by the base.
The area of any triangle is equal to half the base multiplied
by the perpendicular height.
The perpendicular height of any equilateral triangle is
equal to one of its sides multiplied by 0.866.
The area of any equilateral triangle may be found by mul-
tiplying the square of one of the sides by 0.433.
Example.
Find the area of an equilateral triangle when the sides are
12 inches long.
Solution:
Area = 12 X 12 X 0.433 = 62.352
The side of any equilateral triangle multiplied by 0.6582
gives the side of a square of the same area.
The side of any equilateral triangle divided by 1.3468 gives
the diameter of a circle of the same area.
To Figure the Area of Any Triangle when Only the
Length of the Three Sides is Given.
Rule.
From half the sum of the three sides subtract each side
separately ; multiply these three remainders with each other
and the product by half the sum of the sides, and the square
root of this result is the area of the triangle.
Example.
Find the area of a triangle having sides 12 inches, 9 inches
and 15 inches long.
Solution
:
Half the sum of the sides = 18
Area = V(18 — 12) X (18 —9) X (18 —15) X IS
Area = \A) X 9 X 3 X 18
Area = V2916
Area = 54 square inches.
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