MENSURATION.

In the following formulas, the letters have the meanings here given, unless otherwise stated.

D =

d

R

=

=

larger diameter;

smaller diameter;

radius corresponding to D;

= radius corresponding to d;

P = perimeter or circumference;

C = area of convex surface area of flat surface which can

be rolled into the shape shown;

Sarea of entire surface

=

C+ area of the end or ends;

=

π = 3.1416, nearly ratio of any circumference to its diam

The other letters used will be found on the cuts.

The above letters refer to angles.

For a right-angled triangle, c being the

hypotenuse,

a

C=

length of side opposite an acute angle

of an oblique-angled triangle.

C = length of side opposite an obtuse angle

of an oblique-angled triangle.

c = √ a2 + b2 + 2b e.

h = Va2 e2.

For a triangle inscribed in a semicircle; i. e., any rightangled triangle,

TRAPEZOID.

Ah(a + b).

TRAPEZIUM.

Divide into two triangles and a trapezoid.

A

bh'a (h' + h) + ch;

or, A= [bh' + ch+ a(h'+h)].

Or, divide into two triangles by drawing a diagonal. Consider the diagonal as the base of both triangles, call its length 1;

call the altitudes of the triangles hi and he; then Al(h1 + h2).

=

*The perimeter of an ellipse cannot be exactly determined without a very elaborate calculation, and this formula is merely an approximation giving fairly close results.

A prismoid is a solid having two parallel plane ends, the edges of which are connected by plane triangular or quadrilateral surfaces.