PROB. VI.

To find the content of a triangular piece of ground.

Multiply the base by half the perpendicular, or the perpendicular by half the base; or take half the product of the base into the perpendicular.

The reason of this is plain, from cor. 2. theo. 12. geom.

EXAMPLE.

PL. 1. fig. 16.

Let ABC be a triangular piece of ground, whose longest side or base BC, is 24C. 38L. and perpendicular AD, let fall from the opposite angle, is 13C. 28L. Required the content.

Ch. L. Ch. L.

Perp. 13.286.78

perp. 6.393.39

}

four-pole chains by prob. 1. sect. 1. pt. 2.

Or 2dly. Perp. 6.78 of four-pole chains.

base 6.19

Or 3dly. Base 12.38 four-pole chains.
Perp. 6.78

9904

8666

7428

83.9364

A. R. P.

Its=4|19682 = 4. 0. 31.

Or the base and perpendicular may be reduced to perches; and the content may be thence obtained, thus:

30

Half the perp. 13.56 By prob. 4. sect. 1. pt. 2.

But, square perches may be reduced to acres, &c. rather more commodiously, by dividing by 40 and 4, than by 160; thus,

410)671

4)16. 31

A. 4. 0. 31

The map may be readily drawn, having the distance from either end of the base, to the perpendicular given; as may be evident from the figure.

PROB. VII.

The content of a triangular piece of ground, and the base given, to find the perpendicular.

Divide the content in perches, by half the base in perches; and the quotient will give you the perpendicular in perches and so in chains.

EXAMPLES.

PL. 1. fig. 16.

Let BC be a ditch, whose length is 24C. 40L. by which it is required to lay out a triangular piece of ground, whose content shall be 4A. 1R. 10P. Required the perpendicular.

Perches. Ch. L.

Answer perp. 27. 28.-13.45.

This perpendicular being laid on any part of the base, and lines run from its extremity to the ends of the base, will lay out the triangle (by cor. to theo. 13. geom.) so that the perpendicular may be set on that part of the base which is most convenient and agreeable to the parties concerned.

PRACTICAL QUESTIONS.

Ex. 1. What is the area of a parallelogram, whose length is 12.25, and its height 8.5 four-pole chains?