MENSURATIONS

MENSURATIONS

1. Square:-figure (1)Area = a2Sq units. (or) P2/16 (2)Perimeter = P =4a (or) a = P/4 (3)Digonal (or)length of the rod that can be placed= a = P/4 2.Rectangle:-figure (1)Area = l*b (2)Perimeter = P = 2(l+b) (3)Digonal = d = Öl2+b2 Þb = Öd2-l2 Þl = Öd2-b2 3.If area of plot is given as 'z'm2 and the ratio of l:b is given as x:y, then length is l = x * [Öz/(x*y)] b = y * [Öz/(x*y)] 4. length required=(length * breadth of a room)/width of the carpet 5. No:of stones =(length * breadth of a room)/(length * breadth of a stone) 6. A2/A1= (a2/a1)2 = (d2/d1)2 7. P2/P1=ÖA2/A1 8.Circle:-figure (1)Area = Pr2 (or) P(d2/4) (2) d = 2r (3)Perimeter (or) Circumference = 2Pr = Pd Where P = 22/7 (or) 3.14 (4) A = c2/(4 P) (or) c = Ö4 PA = 2ÖPA 9. % dec in Area = fs [(r12 - r22)/r12] * 100 10. Distance travelled in 'N' revolutions is, D = N * Pd (or) N = D/(Pd) 11.Area left ungrazed = a2(1 - P/4) 12.Road out of the garden:-figure (1)Area of the road = 2w[l+b+2w] = [(l+2w)(b+2w)]-(l*b) Road inside the garden:-figure (2)Area of the road = 2w[(l+b)-2w] Two parallel roads:-figure (3)Area of the road = w[(l+b)-w] 13.Traingles:- (1)Right angled traingles:-figure Area = (1/2)*b*h d = Öb2+h2 (2)Equilateral traingles:-figure Area= (Ö3/4)a2 Perimeter = P = 3a Height= (Ö3/2)a (3)Scalene traingle:-figure Perimeter = P = 2s=a+b+c Þs=(a+b+c)/2 Area = Ös(s-a)(s-b(s-c) (4)Isosceles traingle:-figure Perimeter = P 2a+b Area = b/4(Ö4a2-b2) 14.Volumes:- (a)Cube:-figure (1)Lateral surface area = 4a2 (2)Total surface area = 6a2 (3)Volume of a solid = Base area * Height = a2 * a = a3 (4)Diagonal (or) Longest pole = d = Ö3a (b)Cuboid:-figure (1)Lateral surface area = AL = 2h[l+b] (2)Total surface area = AT 2[lb+lh+bh] (3)Volume = V = lbh (4)Diagonal = d = Öl2+b2+h2 (5)No:of boxes = (lbh)/l1b1h1 = (Volume of big box)/(Volume of small box) 15. a3 = v13+v23+v33 16. a1/a2 = (v1/v2)1/3 17.No:of boxes(if areas are given) = a3/a13 = (a/a1)3 (18)Cylinder:-figure (1)Lateral surface area = AL = 2Prh (2)Total surface area = AT 2Pr(h+r) (3) AT/Al=(h+r)/h (4)Volume = v = Pr2h (5)Area of each flat surface i.e of ends = Pr2 (19)Cone:-figure (1)Slant height = L = Öh2+r2 (2)Volume of the cone = 1/3(Pr2h) (3)Curved surface area of cone = Prl (4)Total surface area = Pr(l+r) (5) v1/v2=(r1/r2)2 * h1/h2 20. H-h = (4/3) * rs 3/rd2 21.Area of circle inscribed in an equilateral traingle is r2.It's height is, h = 3r (22)Sector:-figure (1) l= (q/360)*2P r (2)A = (q/360)*Pr2 (3)Circumference,c = l+2r (23)Four circular carboard pieces,each of radius 'r'cm are placed in such a way that each piece touches two other pieces.The area of the space enclosed by four pieces is, (2r)2 [1-P/4]cm2 (24)Rhombus:-figure (1) 4a2 = d12 + d22 (2)Area = (1/2)d1d2 (3)Perimeter = P = 4a (25)Parallelogram:-figure (1)Area of DleABC 1/2(bh) (2)Area of DleACD 1/2(b/h) (3)Area of parallelogram = bh (26)Trapezium:-figure (1)Area of Trapezium=Area of (DleABC + DleACD) 1/2(ah) + 1/2(bh) = [(1/2)h][a + b] (27)Sphere:-figure (1)Surface area = 4Pr2 (2)Volume = 4/3(Pr3) (3) A1/A2 = (r1/r2)2 (4) v1/v2 = (r1/r2)3 (5) v1/v2 = (A1/A2)3/2 (6) A1/A2 = (v1/v2)2/3 28.Area of four walls = 2 * (length + breadth) * height