Lines And Plane Surfaces

Lines And Plane Surfaces 148

Triangle

Right Triangle.

Triangle 149

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).

Triangle 150Triangle 151

* 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.

Triangle 152

Parallelogram

Area = ab.

Trapezoid

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

Trapezoid 153Trapezoid 154

Trapezium

Divide into two triangles and a trapezoid.

Area =

Trapezium 155

or, area

Trapezium 156

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:

Name.

No. Sides.

Multiplier.

Triangle

3

.433

Square

4

1.000

Pentagon

5

1.720

Hexagon

6

2.598

Heptagon

7

3.634

Octagon

8

4.828

Nonagon

9

6.182

Decagon

10

7.694

Regular Polygons 157

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}

Irregular Areas 158