Note. Twice the area divided by the perpendicular gives the base, and twice the area divided by the base gives the perpendicular. Ex. I. Find the area of a triangle whose base is 24 ft. Ex. 2. Find the area of a triangle whose base is 1875 links, and perpendicular 1476 lks., and the rent at 35s. per I. EXAMPLES. Find the area of a triangle whose base is 9 ft. 8 in., and perpendicular 7 ft. 4 in. Ans. 354 feet. 2. Find the area of a triangle whose base is 517 yards, and perpendicular 341 yards. Ans. 18 a. or. 34 P. 3. The area of a triangle is 7 a. 3 r. 14 p., and the base is 9 chains; find the perpendicular. Ans. 16 chains. 4. Find the rent of a triangular field whose base is 2220 links, and perpendicular 3330 links, at 35s. per acre. Ans. £64. 13s. 8d. 5. The base and perpendicular of a triangle are 120 and 48, and the perpendicular from one of the angles at the base on the opposite side is 72; find the other two sides. Ans. 80 and 73'756. 6. Find the area of an equilateral triangle whose side is 56 yards. Ans. 443 P. THE TRAPEZIUM. VI. To find the area of a trapezium when the diagonal and the perpendiculars upon it from the opposite angles are given. Multiply the sum of the perpendiculars by the diagonal, and divide by 2. Ex. I. Let ABCD be a trapezium, of which the diagonal is AC, and BE, DF perpendiculars upon AC from the opposite angles B, D. Let AC=324 yards, BE=194 yards, and DF=245 yards. 245 194 439 324 1756 878 1317 2 142236 4840 71118 (14 a. 2 r. 31 p. 4840 22718 19360 1210) 3358 2420 938 40 3752 122 121 I Ex. 2. Find the value of a board in the form of a trapezium, whose diagonal is 5 ft. 9 in., and perpendiculars upon it from the opposite angles, 4 ft. 6 in., and 6 ft. 8 in., at Is. 9d. per square yard. I. The diagonal of a trapezium is 18 ft. 4 in., and the perpendiculars upon it from the opposite angles are 10 ft. 6 in., and 12 ft. 8 in. Find the area. Ans. 2123 sq. ft. 2. The diagonal of a trapezium is 93 chains, and the perpendiculars upon it are 61 and 103 chains; what will it cost mowing at 8s. 6d. per acre? Ans. £3. 8s. IId. nearly. 3. The area of a trapezium is 16 a. 3 r. 8 p., the diagonal 16 chains, and the perpendiculars upon it are in the ratio of 5 to 7; find the perpendiculars. 4. Ans. 8, 121 chains. ABCDE is a five-sided figure; the diagonal AD is 7 chns. 15 links, and the perpendiculars from C and E upon it are 4 chns. 12 lks., and 5 chns. 62 lks.; 57 lks., BC Ichn. 65 lks., and the angle. Find the area. AB is 5 chns. angle ACB is a right Ans. 3 a. 3 r. 2744 P. |