a. Area of a rectangle = (length × breadth) b. Perimeter of a rectangle = 2 (length + breadth) ***Square :- a. Area of square = (side)2 b. Area of a square = ½ (diagonal)2 Area of 4 walls of a room = 2 (length + breadth) × height ***Triangle :- a. Area of a triangle = ½ × base × height b. Area of a triangle = , where s = ½ (a + b + c), and a, b, c are the sides of the triangle c. Area of an equilateral triangle = / 4 × (side)2 d. Radius of incircle of an equilateral triangle of side a = a / 2 e. Radius of circumcircle of an equilateral triangle of side a = a / ***Parallelogram***Rhombus***T rapezium :- a. Area of a parallelogram = Base × Height b. Area of a rhombus = ½ × (Product of diagonals) c. The halves of diagonals and a side of a rhombus form a right angled triangle with side as the hypotenuse. d. Area of trapezium = ½ × (sum of parallel sides) × (distance between them) **Circle***Arc***Sector :- where R is the radius of the circle: a. Area of a circle = πR2 b. Circumference of a circle = 2πR c. Length of an arc = Ө/360 × 2πR d. Area of a sector = ½ (arc × R) = Ө/360 × πR2 ***Cuboid :- Let length = l, breadth = b & height = h units Then, a. Volume = (l × b × h) cu units b. Surface Area = 2 (lb + bh + hl) sq. units c. Diagonal = units ***Cube :- Let each edge of a cube be of length a. Then, a. Volume = a3 cu units b. Surface Area = 6a2 sq. units c. Diagonal = ( × a) units ***Cylinder :- Let radius of base = r & height (or length) = h. Then, a. Volume = (πr2h) cu. units b. Curved Surface Area = (2πrh) sq. units c. Total Surface Area = 2πr(r + h) sq. units ***Cone :- Let radius of base = r & height = h. Then, a. Slant height, l = units b. Volume = (⅓ πr2h) cu. units c. Curved Surface Area = (πrl) sq. units d. Total Surface Area = πr(r + l) sq. units ***Sphere :- Let the radius of the sphere be r. Then, a. Volume = (4/3 πr3) cu. units b. Surface Area = (4πr2) sq. units ***HemiSphere :- Let the radius of the sphere be r. Then, a. Volume = (2/3 πr3) cu. units b. Curved Surface Area = (2πr2) sq. units c. Total Surface Area = (3πr2) sq. units
Posted on: Mon, 18 Aug 2014 13:08:25 +0000
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