214. If a foundation is 25' X 32', how large ought the bottom of the excavation to be to allow for a footing course and a tile drain?

215. What is the length of a brace completing a triangle, the sides of which are 9.295' and 14' long?

216. Which will have the more sectional area, an 8" X 8" sill, with a 2" X 4" and a 2" X 2" mortise, or a 6" X 8", with no mortising, and a 2" X 4" spiked on to support floor joists, and how much greater?

217. If a girt is 8" X 8", and 2 floor joists are mortised into it each with a 2" X 4" tenon, what is the actual area of the girt?

218. What is the length of a brace completing a triangle each side of which is 4' 6" long?

219. What is the length of a balloon brace for sides 30" X 12' long?

220. If a floor is well bridged, and a load of 12,000 lb. causes a deflection of 1/16", what would be the deflection if the floor were not bridged?

221. What is the greatest square which can be contained in a 24" circle?

222. What will be the size of a square 1/2 of the area of one measuring 10' upon each side?

223. What will be the diameter of a circle which will equal the area of two given circles, one 5' and the other 8' in diameter?

224. If an octagon is 5' upon one side, what is its width?

225. If a hexagon is 5' 11 1/4" upon each side, what is its width?

226. What is the length of the diagonal of an octagon which is 5' upon a side?

227. What will be the rise of a half pitch roof, if the house is 28' wide?

Note. - In problems 228, 229, 230, estimate the width of the shingled area of each side of the roofs, to equal the next larger foot than the actual dimensions.

228. If the above roof has a projection of 18" and the house is 35' long, how many shingles will be needed to cover the roof, allowing 1000 per square, the rafters being 2' longer than the actual length?

229. A third pitch roof house 28' X 36' 9", with a lookout of 18" horizontal projection, is to be covered with a steel roof at a cost of $3 per square. What will it cost?

230. The roof of a quarter pitch house, 30' X 28', with a lookout of 12" horizontal projection, is to be painted at a cost of $1..25 per square. What will it cost?

231. What is the length of a rafter of a half pitch roof, if the house is 29' wide?

232. If the rafters are to be set 24" to centers, how many will be required for a roof which is 40' long?

233. What will be the length of the common rafter of a half pitch roof if the house is 24' wide?

234. What will be the rise and run of the common rafter of a third pitch roof of a building 32' wide?

235. What will be the length of a common rafter of a two-thirds pitch roof if the house is 24' wide?

236. What will be the length of a common rafter of a third pitch roof of a house which is 27' wide?

237. If a hip roof is to be built upon a house which is 28' square, will there be any ridge?

238. If a hip roof house is 26' wide and 29' long, how long will the ridge be?

239. If a ridge 2' 11" long extends to take the entire side cut of the hip rafters, what will be the entire length of it?

240. If a 1 3/8" ridge board is used, how much shorter will each end of the ridge be? Give the answer to the nearest 1/12 of an inch.

241. A shed roof rises 12" to 12'. Allowing 1' for lookouts, what will be the entire length of the rafter?

242. What will be the entire rise of the roof from eaves to eaves?

243. What will be the length of the lookouts of a half pitch roof, which projects 22"?

244. What will be the length of the hip rafter of a half pitch house 24' wide?

245. What will be the length of the hip rafter of a third pitch house 28' wide?

246. What will be the length of the hip rafter of a quarter pitch house 25'11" wide?

247. What will be the length of a hip lookout for a third pitch house, if the common rafters project 18"?

248. How much shorter will a quarter pitch hip rafter be cut if a 2" ridge is used, the ridge taking the entire joint of the hip?

249. What will be the length of the collar beam for a half pitch house, if the bottom is placed 6' below the apex of the roof?

250. Find the same for a third pitch house.

251. Find the same for a fourth pitch house.

252. What will be the length of the strut which supports the common rafter of a quarter pitch roof? It is square with the rafter and 6 ft. from the end.

253. Find the same for a third pitch house.

254. Find the same for a quarter pitch house.

255. An octagonal tower is to be built, 6' upon each side. What is the parallel width of the tower?

256. What is the diagonal of the above tower?

257. What is the length of the hip rafter of the above tower, if it is 10' high at the apex?

258. If a 6" king post is used, how much will each hip rafter be shortened?

259. The common rafters of the roof of an addition are to be cut to dimensions instead of an ordinary pitch. If the run of these rafters is 10' 7", and the rise 6' 4", what will be their length?

260. If a hexagonal tower 8' upon one side is to be built, what is its diagonal?

261. What will be the parallel width of the above tower?

262. What will be the length of the hip rafter if the above roof rises 12'?

263. If a circular roof 22' in diameter and 11' high is to be built, what will be the length of the first pair of rafters?

264. Find the length of the second pair.

265. Find the lengths of the third and fourth pairs.

266. What will be the length of the valley rafter of a third pitch house, which is 24' wide, an ell 20' wide joining the main house?

267. If a 2" hip is used, how much shorter will the valley rafter be?

268. If the common rafters of a half pitch roof meet at the apex and jacks are to be 2' to centers, how much shorter will the first jack be than the common rafter?