Fig. 21. - Plan of Hip Roof with Deck.

Fig. 22.-Side Elevation of Roof shown in Fig. 21.

Fig. 23. - Size and Shape Necessary to Cover Roof.

Fig. 24. - Plan of Pyramidal Roof.

Fig. 25. - Plan of Roof which Hips to a Ridge.

The liability to error in estimating the area of hip roofs is still greater than in the case of gable roofs, for no matter from which point we view the elevations the length of the common rafter is not shown in proper position to indicate the true size of the roof. Fig. 21 shows a plan of a hip roof with deck, and Fig. 22 a side elevation of this kind of roof. In this figure some might take the lines A B and C D for the length of the hips, and C E for the length of the common rafter, but such is not the case. C D shows the length of the common rafter as we would see it on the end looking at the side view, hence E D is the run, E C the rise and C D length of common rafter. I will now indicate the method of developing the lengths of the hips, showing the true size of the roof, and how to reduce the figure to a rectangle of equal area. Referring to Fig. 23, A B C D and E represent the same lines as shown in Fig. 22. Now, take the length of the common rafters A B and C D in Fig. 23 and draw them perpendicularly, as shown by E F and G H. Connect F with D and H with A for the length of the hips, then the figure inclosed by the lines A H F D will be the size and shape of the roof necessary to cover the side elevation. The triangle described by the lines D E F equals in area the triangle A I H, shown by the dotted lines. Hence the roof A H F D is equal in area to the rectangle A I F E, whose length is one-half the sum of the eaves and deck lengths and whose breadth is the length of the common rafter. The length multiplied by the breadth gives the area. From the foregoing illustrations and principles we derive the following:

Rule. - Add the lengths at the eaves and deck together, divide by two and multiply by the length of the common rafter. The area of the deck is found by multiplying the length by the breadth.

Example. - What is the area of a hip roof 20 x 28 feet at the eaves, with deck 4 x 8 feet, the length of the common rafter being 10 feet ?

Operation. - 20 + 4+20 + 4 +28 + 8 + 28 + 8 ½ 2 x 10 = 600 feet, the area of the four sides. 4 x 8 = 32 feet, the area of the deck. 600 + 32 = 632, the total area of the roof.

This rule will apply to hip roofs of most any kind. If the roof is pyramidal in form and hips to a point, as shown by Fig. 24, then there is nothing to add for deck, and we simply multiply one-half the length at the eaves by the length of the common rafter. The principles of the three forms of hip roofs are essentially the same.