In the measurement of carpentry work there is probably no part so difficult to master as the accurate measurement of roofs, particularly where they are composed of hips and valleys forming a great variety of irregular surfaces. The shapes of roofs having hips, valleys and gables are usually represented in the form of some triangle. The different forms of triangles are shown in the diagrams, Fig. 6 representing an equilateral triangle, Fig. 7 an isosceles triangle, Fig. 8 a right-angled triangle, Fig. 9 an obtuse-angled triangle and Fig. 10 a scalene triangle. Figs. 6, 7 and 10 are also acute-angled triangles. Fig. 11 shows a square and Fig. 12 a rectangle. It is a very easy matter to compute the area or surface measurement of a square or a rectangle. The area of a square or a rectangle is found by multiplying its length by its breadth. In computing roof measurements all triangles can be reduced to squares or rectangles of equal areas by very simple methods.

Figs. 6-10. - Different Forms of Triangles.

Fig. 11. - A Square.

Fig. 12. - A Rectangle.