To find the area of a triangle, its base, and perpendicular height being given.
Multiply the base by the perpendicular height, and half the product will be the area.
Example.—Required the number of square yards contained in a triangle, whose base is 20 yards, and perpendicular height 14 yards.
20 × 14 2 = 140 square yards. Area required.
To find the area of a triangle, whose three sides are given.
From half the sum of the three sides, subtract each side severally; multiply the half sum, and the three remainders together, and the square root of the product will be the area required.
Example.—Required the area of a triangle, whose sides are 50, 40, and 30 feet.
50 + 40 + 30 2 = 60, half the sum of the three sides.
60 - 30 = 30 First difference.
60 - 40 = 20 Second difference.
60 - 50 = 10 Third difference.
30 × 20 × 10 × 60 = 360000.
Square root of 360000 = 600. Area required.
Two sides of a right-angled triangle being given, to find the third side.
1. When the two sides forming the right angle are given, to find the hypothenuse, or side opposite the right angle.