Basic Formula In Maths

(pi = = 3.141592...) Areas

square = a2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2)

circle = pi r 2

ellipse = pi r1 r2

triangle = (1/2) b h equilateral triangle = (1/4) (3) a2 triangle given SAS = (1/2) a b sin C triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula) regular polygon = (1/2) n sin(360°/n) S2 when n = # of sides and S = length from center to a corner Volumes

cube = a3

rectangular prism = a b c

irregular prism = b h

cylinder = b h =

r2 h

pyramid = (1/3) b h

cone = (1/3) b h = 1/3

sphere = (4/3)

r2 h

r3

ellipsoid = (4/3) pi r1 r2 r3 Surface Areas

cube = 6 a2 prism: (lateral area) = perimeter(b) L

(total area) = perimeter(b) L + 2b

sphere = 4

r2

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Area 1. The area of a circle = πr² (π = 3.1416, r stands for radius).

The area of a square = a² (a is the length of a side). The area of a rectangle = length X width. The area of a triangle = ½ X base X perpendicular height.

Surface Area 2. The surface area of a cube = 6a² (a is the length of a side).

The surface area of a rectangular prism = 2hw + 2hl + 2lw (h is height, w is width, l is length).

Volume 3. The volume of a cube = a³ (a is the length of a side).

The volume of a rectangular solid = length X width X height. The volume of a cylinder = πr²h (r is radius of the circle atop the cylinder and h is the height).

Perimeter 4. The perimeter of a square = 4x (x is the length of a side).

The perimeter of a rectangle is 2 X (length of the long side of the rectangle + length of the short side). The perimeter of a triangle = a X b X c (a, b and c are the length of one of the triangle's side). The circumference of a circle = 2πr.

Algebraic 5. (a + b)² = a² + 2ab + b².

(a - b)² = a² - 2ab + b². (a + b + c)² = a² + b² + c² + 2(ab + bc + ca). Shapes Formula

Rectangle: Area = Length X Width A = lw Perimeter = 2 X Lengths + 2 X Widths P = 2l + 2w Parallelogram Area = Base X Height a = bh Triangle Area = 1/2 of the base X the height a = 1/2 bh Perimeter = a + b + c (add the length of the three sides) Trapezoid

Perimeter = area + b1 + b2 + c P = a + b1 + b2 + c

Circle Try the Online tool. The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles. d = 2r c = pd = 2 pr A = pr2 (p=3.14) Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh

Prisms Volume = Base X Height v=bh Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)

Cylinder Volume = pr2 x height V = pr2 h Surface = 2p radius x height S = 2prh + 2pr2

Pyramid V = 1/3 bh b is the area of the base Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases. Cones Volume = 1/3 pr2 x height V= 1/3 pr2h Surface = pr2 + prs S = pr2 + prs =pr2 + pr

Sphere Volume = 4/3 pr3 V = 4/3 pr3 Surface = 4pr2 S = 4pr2