Let A B C represent a right-angled triangle, as shown in Fig. 15. If we divide the triangle horizontally half way on the perpendicular, then the triangle E B D will equal in area the triangle shown by the dotted lines A F E ; hence the triangle A B C equals in area the rectangle A F D C. From the illustra-tion we derive the following: Rule. - Multiply the base by one-half the perpendicular hight.

Fig. 15. - Finding Area of a Right-Angled Triangle.

Fig. 13. - Finding Area of a Scalene Triangle.

In Fig. 16 A B C represents a scalene triangle which has no perpendicular line in reality, but for convenience in estimating we draw one, which is B D, dividing the triangle into two right-angled triangles of unequal areas. By dividing the triangle horizontally half way on the perpendicular, as shown by E F, the triangle E B F equals in area the two triangles shown by dotted lines A G E and F H C.

Hence the triangle A B C equals in area the rectangle AG H C.

Having shown how triangles may be reduced to squares and rectangles of equal areas, the next step will be to show their proper application to roof measurements.