Fig. 10
The area of the triangular portion a c b is equal to the slope length of d c (found by laying off c′ c equal to the height of the ridge above the eaves and drawing c′ d) multiplied by the length of the eaves line a b and divided by 2. Multiplying the dimensions 13.5 feet and 23 feet, respectively, and dividing by 2, the area is found to be 155.3 square feet.
The area of the trapezoid g f i h is half the sum of f i and g h (shown in their true length on the plan) multiplied by the true length of h i. The latter is found by marking the height of the gable i i′ on the ridge line, and drawing the line i′ h, which measures 10.6 feet. Performing these operations, there results
| 5 + 14 | × 10.6 = 100.7 square feet |
| 2 |
for each side, or 201.4 square feet for both. As each of the side gables is the same size, the area of the two roofs is 201.4 × 2 = 402.8 square feet.
The area of the polygon q p n k is equal to the triangle q p w minus the triangle k n w, the area covered by the intersecting gable roof. The former is equal to the triangle a c b, the area of which is 155.3 square feet. The area of k n w is equal to half of n w, or 6.5 feet, multiplied by the true length of k s or the altitude of the triangle; the latter is obtained by laying off k k′ equal to the height of the gable, 5.5 feet, at right angles to k s, and drawing s k′, which is the required altitude and which measures almost 7.4 feet. Then k n w = 6.5 × 7.4 = 48.1 square feet; whence q p n k equals 155.3 - 48.1 = 107.2 square feet.
The area of a p q c is
| a p + q c |
| 2 |
multiplied by the true slope length of t v, or t v′, which measures 15.2 feet. Substituting dimensions, the area is found to be
| 6 + 24 | × 15.2 = 228 square feet. |
| 2 |