CIVIL ENGINEERS FREQUENTLY USING MATHEMATICAL FORMULA

01. SQUARE Area = A * A A – Length of one side 02. RECTANGLE Area = L * B L - Length B - Breadth 03. CIRCLE Area = p*R*R               2 R- Radius of the Circle 04.EQUILATERAL TRIANGLE h = ( a * Ö3) /2 A = (a2 * Ö3) / 4 B - Base of The Triangle H – Height of the Triangle 5. ISOSCELES TRIANGLE Area = c/4*sqrt (4a2 – c2) ac - Base of The Triangle a – Side of the Triangle 06. PARALLELOGRAM Area = B * H B – Base length H – perpendicular Ht of Parellogram 07. TRAPEZOID Area = (A+B)*H H- Perpendicular distance btn Parallel sides 08. SECTOR OF CIRCLE Area = Q*p*R2               360 Where Q = Angle of the Sector R = Radius of the Circle 09. AREA OF RHOMBUS: Area = d1d2             2 Where d1 and d2 are the diagonals. 10. SEGMENT OF CIRCLE: A segment of the circle is that part of the circle contained between the arc and its chord. Area = 2*L*H          Where L- Length of the Area    H - Rise of the arc 11. QUADRILATERALS: A=0.5*d (p1 + p2) Where A = area; d = Diagonal; p1 and p2 are the offsets of the Diagonal. 12. REGULAR HEXAGON: A = (3 a2 Ö3)/2 Where A = area; a = side of the Hexagon 13 REGULAR OCTAGONS: A = 2 a2 (1+Ö2) Where A = area; a = side 14 REGULAR DODECAGONS (12 SIDES): A = 6 a2 Ö(7/4  + Ö3) Where A = area; a = side 15 ELLIPSE: A  = Õ ab         C=DM Where A = area; a = semi-major axis; and b= semi- minor axis; C= Circumference; multiplier.  If value of d/D = 0.2,0.3,0.4,0.5,0.6,0.7,0.8,and 0.9 then the corresponding multiplier (M) sill be 2.1010,2.1930,2.3013,2.4221,2.5527,2.6912,2.8361, and 2.9866 respectively.   D= a*2 and d=2*b. 11. IRREGULAR SURFACES: Divide the area or Figure into an even number (n) of parallel strips by means of (n+1) ordinates, spaced at equal distances, d. Let the ordinates be yi A. TRAPEZOIDAL RULE: Area = d*((y0+yn)/2 + y1 +y2 +…+yn-1) B. DURAND’S RULE: Area = d*[0.4(y0 + yn) + 1.1(y1+yn-1)+y2+y3+…. +yn-1] C. SIMSONS RULE: Area = d*[( y0 + yn ) +4*(y1 + y3 +…..+yn-1) +2*(y2 + y4 + …… +yn-2)] VOLUME: 1.CIRCULAR CONES: A Cone is a solid whose base is a circle and whose convex surface tapers uniformly to a point called the vertex. Volume          = 1/3 X area of base X Vertical Ht. Convex Area = ½ X Perimeter of base X Slant Ht. 2.RECTANGULAR SOLIDS: i)              V = abc ii)             V = A1c = A2b = A3a iii)            V = Ö (A1A2A3) iv)           V = 2 (ab + bc+ ca) v)            D = Ö(a2+b2+c2) Where V= Volume’; S = Whole surface; a = length; b- breadth; c = Depth; A1=Area of base; A2 = area of side; A3 = area of end; d = diagonal. 3.CUBES: i)              V = a3 ii)             S = 6 a2 iii)            D = a Ö3 Where V = Volume; S = Whole surface; a = edge; D = Diagonal. 4.CYLINDERS: i)              V = Õ r2 h ii)             S = 2 Õ r (h+r) Where V =Volume; S = whole Surface; r= the radius of base; h = height. 5.CYLINDRICAL RINGS: i)                       V = Õ2/4 (R+r) (R- r) 2 ii)                     V = 1/32Õ  (C + c) (C – c) 2 iii)                    S = Õ2  (R2 – r2) iv)                   S = ¼ (C2 – c2) Where V = Volume; S= Whole Surface; R= Outer radius; r=inner radius; C= Outer Circumference;    c = Inner circumference. 6.PYRAMIDS AND CONES: V = 1/3 Ah Where V = Volume; A = area of base; h= height. 7.REGULAR TETRAHEDRONS: i)              V = (2*Ö2/3) a3 ii)             S = 4 a2 Ö3 iii)            H = 2aÖ(2/3) Where V = Volume; S = Whole Surface; 2a= edge; h= height 8.FRUSTRA OF PYRAMIDS, CONES and TRAPEZOIDAL VOLUME: V= H/3 (A1 + A2 + Ö(A1 + A2) Where V= Volume; h= height; A1 and A2 are the ends; P and p are the perimeters of the ends; s = slant height. 9.FRUSTRA OF RIGHT CIRCULAR CONES: i)              V= Õh/3 (R2 + r2 + Rr) ii)             S = 0.5 s (C + c) iii)            S = Õ s (R + r) Where V = Volume; S = Curved Surface; R and r are the radii of the ends; C and c are the circumferences of the ends; s = slant height; h= perpendicular height. 10.SPHERES: i)              V = Õ d3/6 ii)             V = 4/3 Õ r3 iii)            S = Õ d2 iv)           S = 4Õ r2 Where V = Volume; S = Surface; d= Diameter; r = radius. 11.SPHERICAL SHELLS: i)              V = Õ/6 (D3 – d3) ii)             V = 4Õ/3 (R3 – r3) Where V = Volume; R=Outer radius; r = inner radius; D = Outer diameter; d= inner diameter; 12.ZONES OF SPHERES: i)              V = Õ h/3 [3(r1 2 + r22)+ h2] ii)             S = Õdh Where V = Volume; S = Curved surface; r1 and r2 are the radii of the two ends; h = height; d = dia of the sphere. 13.Square of the same area as a circle Side = diameter X 0.88623 14.Circle of the same area as a Square Diameter = side x 1.12838 15.PARABOLAS AND PARABLOIDS: Area of space within the parabola = Base x 2/3 perpendicular height Volume of parabloid (Solid) = ½ Õr2h Where r = radius of the base of the paraboloid h = height