Fig. 27   Front Elevation of Roof Shown in Fig. 26.

Fig. 27 - Front Elevation of Roof Shown in Fig. 26.

Fig. 28   Plan of Roof with Four Gables.

Fig. 28 - Plan of Roof with Four Gables.

Let Fig. 26 represent the plan of a building having a roof of three gables of equal size and one smaller gable hipped on the rear side, as shown in the diagram. Fig. 27 shows this roof as it would appear in the front side elevation. Referring now to Fig. 28, A B and B C represent the length of rafters on the front gable. Next set off the length of the common rafters of both the right and left gable perpendicularly, as shown by F G and D E, connecting E with G for the ridge line. On the perpendicular line of the front gable set off the length of the common rafter, shown by the dotted line J H.

Fig. 23.   Diagram for Finding Area of Hoof Shown in Previous Figure.

Fig. 23. - Diagram for Finding Area of Hoof Shown in Previous Figure.

Fig. 29.   .Appearance of Roof in Bight End Elevation.

Fig. 29. - .Appearance of Roof in Bight End Elevation.

Connect H with A and C for the valley rafters, which completes the profile of this side of the roof. The two figures, now represented by A D E H and C F G H, are termed trapezoids. To find the area of a trapezoid multiply half the sum of the parallel sides by the altitude. In this case to make the matter plain we multiply half the length at the eaves and ridge by the length of the common rafter, which gives the area of the roof necessary to cover the elevation shown in Fig. 27.

Fig. 30.   Diagram for Finding Area of Roof Shown in Fig. 29.

Fig. 30. - Diagram for Finding Area of Roof Shown in Fig. 29.

Fig. 29 shows the roof as it would appear in the right end elevation. We will now develop the shape of the roof and obtain the necessary lengths for finding the area of this elevation. Referring now to Fig. 30, A B and B C represent the length of rafters on the right gable. Next set off the length of rafter on the front gable shown by D E. Then set off the same length in the center of the left gable shown by the dotted line J H. Connect H with E for ridge line of front gable. Connect H with A and C for the valley rafters. Now take half the width of the rear gable, which is to be hipped on the end, and in this case is represented by C F From C erect a perpendicular the length of the common rafter on this part, shown by the dotted line C G. Connect G with F for the hip rafter and draw the ridge line G 1 parallel with C F, which completes the profile of this view of the roof. The figure shown by A D E H is a trapezoid, and its area may be found as has been previously described for such figures. The figure shown by C F G 1 is termed a rhomboid. Its area may be found by multiplying C F by C G, or, in other words, the length at the eaves multiplied by the length of the common rafter gives the area. The areas of the two figures added completes the area of the roof necessary to cover the end elevation shown in Fig. 29. As the left end elevation is similar to the right in shape and size the last estimated area doubled will give the area of the roof necessary to cover the two end elevations.

Fig. 31.   Roof as it Appears in Rear Elevation.

Fig. 31. - Roof as it Appears in Rear Elevation.

We have now to consider the rear elevation and the roof necessary to cover it. Fig. 31 shows the roof as it would appear in the rear elevation. We will now develop the shape of the roof and obtain the necessary lengths and lines for finding the area of this elevation. Referring to Fig. 32, A B and B C represent the length of the common rafters on the rear gable.

Fig. 32.   Diagram for finding the Area of Roof Shown in Fig. 31.

Fig. 32. - Diagram for finding the Area of Roof Shown in Fig. 31.

From the center of the gable set off the length of the common rafter, as shown by the dotted line J H. Connect H with A and C for the length of the hips. Set off the length of the common rafter on the right and left gable, as shown by F G and D E ; connect E and G for the ridge line, which completes the profile of the rear view of the roof. It will be seen that the ridge of the rear gable does not come up even with the ridge of the other two ; hence the rear elevation shows a different shape than the front. For convenience in estimating, we divide the roof in the center of the gable, shown by the dotted line H I; then divide the roof perpendicularly each side of the gable, as shown by the dotted lines A K and C L. We now have the roof divided into four figures, of which D E K A and C L G F are rectangles, A K I H and C L I H are trapezoids. As the method of obtaining the areas of such figures has been previously described, further explanation is unnecessary. It has now been shown how to find the area of each side of the roof, as indicated in the plan, Fig. 26. By adding the area of the four sides the total area of the roof will be obtained.