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 From this deduct the area of _y z u_, which is the portion covered by the intersecting gable roof. The true length of _t u_ along the slope is _t u′_, measuring 12 feet; hence, the area of _y z u_ is 14 × 12 ------- = 84 square feet. 2 The net area of _a p q c_ is therefore 228 - 84 = 144 square feet; _b c q w_ being equal to _a p q c_, its area is the same, making the area of both sides 288 square feet. The area of _k n m l_ is _m n_ + _l k_ -------------- × _m l′_, 2 the slope length of _m l_. Substituting dimensions, the area is 11 + 16 ------- × 8.5 = 114.8 square feet. 2 As _k l x w_ is equal to _k n m l_, the area of both is 229.6 square feet. Adding the partial areas thus obtained, the sum is 155.3 + 402.8 + 107.2 + 288 + 229.6 = 1,182.9 square feet, or approximately 11.9 squares. PLASTERING