 Geometry Formulas, Area and Volumes, Cube, Cuboid, Cylinder, Hemisphere, Cone, Sphere,Frustum, Online Help

Area of some rectilinear figures

• Area of a Triangle : 1/2 x Base x Heights
• Area of Equilateral Triangle : Sqrt(3)/4 x (Side)2
• Area of a Triangle – Hero’s formula :
• Sqrt{s (s – a) (s – b) (s – c)} where 2s = a + b + c.
• Area of Rectangle = Length x Breadth
• Area of a Square = (Side)2
• Area of Four Walls = 2 x height (Length + breadth)
• Area of Rhombus = 1/2 x (Products of Diagonals)
• Area of Trapezium = 1/2 x (Sum of Parallel Sides) x (Distance between Parallel lines)
• Area of Parallelogram = Base x Altitude
• Somestandards units of Area
• 100mm2 = 1 cm2, 100 cm2, = 1 dm2
• 100dm2 = 1 m2, 100 m2, = 1 are
• 100arcs = 1 hactare
• 100 hactare = 1 km2

Area related to Circles:

 Circumference of a Circle or Perimeter of a Circle: The Distance arround the circle or the length of a circle is called its circumference or perimeter. Circumference (Perimeter) of a circle = d or 2 r, where, r is the radius of the circle and = 22/7 Circle: If r be the radius of a circle, and its center is O. Area of a Circle = r2 Area of a Semi-Circle =  r2 Area of a Quadrant =  r2 Perimeter of a Semi Circle: If r be the radius of a circle, and its center is O. Perimeter of a Semi Circle : r + 2r Area of a Ring: If r be the radius of a circle, and its center is O. Area of a ring or Annulus : (R2 – r2) Length of arc: Length of arc AB = or Area and Perimeter of a Sector : Area of a Sector OACBO = or (l x r) Area of a Sector OACBO = Length of arc AB + 2r Area of a Segment : Area of a Minor Segemnt ACBA : Area of a sector OACBO – Area of Triangle OAB = – r2sin(theta) Area of a Major Segment BDAB : Area of a circle – Area of a minor segment ACBA = r2 – Area of minor segment ACBA

Surface Area and Volumes:

 Cuboid: If the length of a cuboid is l, breadth is b (sometimes we also use breadth as width ‘w’) and the height is ‘h’. The formula for the lateral surface area, total surface area and its volume of a cuboid are Lateral Surface area of a Cuboid= Area of four walls = 2 (length + breadth) x height = = 2 (l + b) x h Total Surface area of a Cuboid = 2 (length x breadth + breadth x height + height x length) = 2 (lb + bh + hl) Volume of a Cuboid = length x breadth x height = lbh Cube : Basically a cube is a special type of a cuboid in which length, breadth and its height are equal i.e. length = breadth = height and it is also called an edge of a cube. The formula for the lateral surface area, total surface area and its volume of a cube are Lateral Surface area of a Cube = Area of four walls = 4 (edge)2 Total Surface area of a Cube = 6 x (edge)2 Volume of a Cuboid = (edge)3 Right Circular Cylinder : It the radius of a right circular cylinder is ‘r’ and its height is ‘h’. Then the curved surface area, total surface area and volume formula is given by Area of the base of a cylinder = r2 Area of curved surface = Lateral surface area = Perimeter of the base x Height of cylinder Total surface Area = 2 rh + 2 r2 = 2 r (h + r) Right Circular Hollow Cylinder : If the radius of internal and external cylinder is ‘r’ and ‘R’ respectively. Then the formula for curved and total surface area, volume of a hollow cylinder is given by Area of curved surface = (Area of External Surface) + (Area of Internal Surface) = 2 Rh + 2 rh Total Surface Area = Curved surface area + 2 (Area of the base ring) = (2 Rh + 2 rh) + 2( R2 – r2) = 2 (R + r) (h + R – r) Volume of a hollow cylinder : Exterior Volume – Internal Volume = ( R2 h – r2h) = h (R2 – r2) Right Circular Cone: If r be the radius, h be the height and l be the slant height of a right circular cone. Then the slant height, area of its curved surface and volume is given by the formula Slant height (l) = √(h2 + r2) Area of a Curved Surface = rl = r √(h2 + r2) Total Surface area = Area of a curved surface + Area of a Base = rl + r2 = r ( l + r) Volume of a cone = 1/3 r2h Sphere: If r be the radius of a sphere. Then the formula for its surface area and its volume is given by Surface Area = 4 r2 Volume = 4/3 r2 Spherical shell : If r be the radius of internal, and R be the radius of external spherical shell. Then the surface area and volume is given by the formula Curved Surface Area = 4 R2 Volume = 4/3 R3 – 4 /3 r3= 4/3 (R3 – r3) Hemisphere: If r be the radius of internal, and R be the radius of external spherical shell. Then the surface area and volume is given by the formula Curved Surface Area = 2 r2 Total Curved Surface Area = Area of curved Surface + Area of its Base = 2 r2 + r2 = 3 r2 Volume = 2/3 r3 Frustum of a Cone : Fructum is a latin word and the meaning is ‘piece cut off’. If any right circular cone is cut off by a plane, which is parallel to its base, then the portion of the cone between the plane and the base of a cone is known as a fractum of a cone.  Then the formula for curved and total surface area, volume of a frustum of a cone is given by Curved Surface Area = l (R + r) where l = √[h2 + (R – r) 2] Total Curved Surface Area = [R2 + r2 + l (R + r)] Volume = 1/3 h [R2 + r2 + Rr] Here : h = Vertical height of the frustum l = slant height of the frustum R = radius of the top r = radius of the bottom