24.20000 Ans. 7 acres 3 roods 8 perches 245 yards. 1050 Ff = 420 Anfo 7 ac. 3 ra 8 per. 24; yds, 7.80500 as before. Required Required the area of the irregular figure ABCDEF, of which the side AB is 40, AC 5C, AD 55, AE 69, AF 36 Scots chains; and the angles are as follow. Plate 6. fig. 80. BAC 40°. METHOD II. By finding the perpendiculars. To find Bb. To find Cc. As rad. 90° 10.00000 As rad. = 90=. 10.00000 is to AB 40 1,60206 is to AC = 50 = 1,69897 So is fine 40° 9,80807 | So is fine 43° 9,83378 To Bb 25.71 1,41013 | To Cc 34.1 = 1.53275 To find Dd. To find Ff. 10,00000 10.00000 is to AD = 55 = 1,74036 is to AF = 36 = 1.55630 So is fine 40° 30' 9,81254 So is fine 48° 20' - 9,87334 To Dd 35,72 1,55290 | To Ff 26.89 = 1,42964 Now, to find the area by bases and perpendiculars. 25.71 X 50 = 1285.5 2)7481,09 twice the area. 10)3740.545 374.0545 Anf. 374.0545 acres, Lx. 3. Required the area of the following polygon, where of the sides are as follow, viz. AF 31.5, ,FE 33.5. ED 25.5, DC 38.5, CB 43.5, BA 34.5, AE 60.5, AD 81.7, BD 74-3 English chains. Anf. 277 acres 3 ro. 12 perches. PROPROBLEM XII. To find the angles of any regular polygont. By cor. ist, I. 32. Euclid. All the anterior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has fides. Hence the following rule. RULE. From double the number of fides fubtract 4, and the remainder is the number of right angles contained by all the fides of the polygon. Multiply the remainder by go, and divide the product by the number of fides, the quot gives the degrees in any of the angles. Ex. 3. Ex. 4. 108 degrees in each angie. Ex. 2. Required the angle of a heptagon. Anf. 128° 347 of a hexagon. Anf. 120. of a decagon. An). 144. Ex. 5: of an octagon. Anf. 135. Ta PRO. PROBLEM XIII. To find the area of a regular polygon. RULE. Find the area of a triangle, constructed on one of the fides of the polygon, and whose vertex is in the centre ; then mul. tiply this area by the number of sides, and the product will be the area of the polygon. Or, Multiply the perimeter by the radius of the inscribed circle, and half the product is the area of the polygon. EXAMPLE I. As rad. 90 = Required the area of a pentagon, whose fide is 10. 11, To find the angle. To find the rad. of the infcribd. 5 10,00000 2 is to EG 5 0,69897 So is tang. 54 = · 10,13874 JO To FG 6,882 = 4 0,83771 6 90 5)540 Angle 103 The perpen. 6,882 5 34.410 No, fides 5 Area 172.050 Ex, 2. Required the area of a hexagon, whose side is 30. Anf. 2338.2 |