5 ⚫6029760 10 ⚫6041356 15 *6052940 20 6064511 25 *6076069 30 6087614 35 •6099147 40 6110666 *7915792 20 40 ⚫6383201 45 •6122173 *7906896 15 45 50 6133666 *7897983 10 50 55 6145147 •7889054 5 55 60 6156615 ⚫7880107 0 60 Nat. Co-s. Nat. Sines. M. ⚫7986355 60 0 ⚫6293204 7771460 60 *6304500 *7762298 55 6315784 •7758121 50 '6327053 7743927 45 6338309 •7734716 40 7942379 35|| 25 6349553 7725489 35 7716246 30 *7924671 25 35 *6371998 7706986 25 7697710 20 •6394390 7688418 15 When the diagonals, and the angle made by their intersection, are given. By logarithms. As radius Is to the s. of made by the diagonals of a parallel ogram, one with another *, So is half the product of the diagonals To the area. • The diagonals of the square and rhombus intersect each other at right angles; therefore their natural sine is 1. The half product of the diagonals will therefore be the area: that is, AC2 AC x BD in the rhombus, the area. 2 in the square, or (See the following fig.) 2 This rule is common to all quadrilaterals. 1. What is the area of a rhomboides, the base of which is 360, its slope end 255 links, and the included ▲ 58° ? 2. What is the area of a rhombus, whose base is 370, and perpendicular breadth 320-4 ? By 1st Rule. 370 x 320-4 = 118548 for the answer. 3. What is the area of a rhombus, whose diagonals are 300 and 200? 300 x 200 2 By the 3d Rule. = 300 x 100 = 30000 for the answer. 4. What is the area of a parallelogram, whose diagonals are 300 and 250, and the angle made by their intersections, equal to 60°? 5. What is the area of a rhombus, whose sides are 700 each, and the included 60° ? Ansr. 424352.446. 6. What is the superficial measure of a square, whose diagonal is 540? See note to Rule 3. Ansr. 145800. 7. Required the area of a rhombus, whose base is 181, and perpendicular 156.8. Ansr. 28380.8 8. What is the area of a rhomboides, whose diagonals are 540 and 325, and the angle of intersection Ansr. 76994.07. 61° 20' ? |