Lines And Plane Surfaces

Triangle

Right Triangle.

Oblique Triangle.

If altitude or height h and base 6 are known:

Area = 1/2 b h.

If the three sides are known:

Let s = 1/2(a + b + c).

* This formula, while given as an exercise in formulas, is also useful in calculating directly the size of a square wooden column, instead of ascertaining it by trial, as is usual.

Parallelogram

Area = ab.

Trapezoid

Area = 1/2h(a + b).

Trapezium

Divide into two triangles and a trapezoid.

Area =

or, area

Regular Polygons

Divide the polygon into equal triangles and find the sum of the partial areas. Otherwise, square the length of one side and multiply by proper number from the following table:

Irregular Areas

Divide the area into trapezoids, triangles, parts of circles, etc., and find the sum of the partial areas.

If the figure is very irregular, the approximate area may be found as follows: Divide the figure into trapezoids by equidistant parallel lines b,c,d, etc. The lengths of these lines being measured, then, calling a the first and n the last length, and y the width of strips,

Area = y{(a+n)/2+b+c+etc+m}