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Geometry Formulas
Geometry is a branch of Mathematics that revolves around shapes, sizes, and relative positions of properties and figures. The section deals with lengths, volumes, and areas. Geometry is of two kinds: Plane Geometry and Solid Geometry. Plane Geometry deals with different shapes, and Solid Geometry calculates the area, length, perimeter, and volume of geometric figures and shapes. Other geometric formulas concern height, radius, surface area, etc.
The students of secondary standards must study geometry formulas extensively to understand the topics indepth. The academic experts at Extramarks have designed a list of all geometry formulas to help the students in their educational courses.
Classwise Most Important Geometry Formulas
Class 8
 Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, where ‘r’ is its base radius and ‘l’ its slant height. ‘l’ = √(r2 + h2)
 Volume of a Cuboid = Base Area × Height = Length × Breadth × Height
 Volume of a Cone = (1 / 3 )πr2h
 Volume of a Sphere = (4/3) π r3
 Volume of a Hemisphere = (2/3) πr3
Class 9
 Surface Area of a Cuboid = 2(lb + bh + hl), where ‘l’, ‘b’ and ‘h’ are the length, breadth, and height respectively.
 Curved Surface Area of a Cone = 1 /2 × l × 2πr = πrl, where ‘r’ is its base radius and ‘l’ its slant height
 Surface Area of a Sphere = 4 π r2
 The volume of a Cuboid = Base Area × Height = Length × Breadth × Height
 The volume of a Cube = a3 where ‘a’ is the edge of the cube.
 The volume of a Cylinder = πr2h, where ‘r’ and ‘h’ are radius and height respectively.
 Volume of a Cone = (1 / 3)πr2h
 Volume of a Sphere = (4/3) πr3
 Volume of a Hemisphere = (2/3) πr3
Class 10
 Volume of Sphere = 4/3 ×π r3
 Lateral Surface Area of Sphere (LSA) = 4π r2
 Total Surface Area of Sphere (TSA) = 4πr2
 Volume of Right Circular Cylinder = πr2h
 Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
 Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
 Volume of Hemisphere = ⅔ x (πr3)
 Lateral Surface Area of Hemisphere (LSA) = 2πr2
 Total Surface Area of Hemisphere (TSA) = 3πr2
 Volume of Prism = B × h
 Lateral Surface Area of Prism (LSA) = p × h
 The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2].
 The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2
Class 11
 Slope m = rise/run = Δy/Δx = y2−y1/x2−x1
 PointSlope Form y−y1 = m (x−x1)
Class 12
 Cartesian equation of a plane: lx + my + nz = d
 Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2)
Basic Geometry Formulas
 Perimeter of a Square = P = 4a
Where a = Length of the sides of a Square
 Perimeter of a Rectangle = P = 2(l+b)
Where, l = Length, b = Breadth
 Area of a Square = A = a2
Where a = Length of the sides of a Square
 Area of a Rectangle = A = l×b
Where, l = Length, b = Breadth
 Area of a Triangle = A = ½×b×h
Where, b = base of the triangle; h = height of the triangle
 Area of a Trapezoid = A = ½×(b1 + b2)×h
Where b1 & b2 are the bases of the Trapezoid; h = height of the Trapezoid
 Area of a Circle = A = π×r2
 Circumference of a Circle = A = 2πr
Where, r = Radius of the Circle
 Surface Area of a Cube = S = 6a2
Where, a = Length of the sides of a Cube
 The curved surface area of a Cylinder = 2πrh
 Total surface area of a Cylinder = 2πr(r + h)
 Volume of a Cylinder = V = πr2h
Where, r = Radius of the base of the Cylinder; h = Height of the Cylinder
 Curved surface area of a cone = πrl
 Total surface area of a cone = πr(r+l) = πr[r+√(h2+r2)]
 Volume of a Cone = V = ⅓×πr2h
Where r = Radius of the base of the Cone, h = Height of the Cone
 Surface Area of a Sphere = S = 4πr2
 Volume of a Sphere = V = 4/3×πr3
Where r = Radius of the Sphere
Type of Geometry Formulas
 Formulas for the perimeter of plane figures
 Formulas for the area of plane figures
 Formulas for the volume of solid shapes
 Formulas for the surface area of solid shapes
How to apply geometry formulae in Mathematics?
The formulas are used to make out the perimeter, breadth, height, area, surface area, and many more.
Let us see an example.
Example: Calculate the area of a trapezium with parallel sides of 24cm24cm and 20cm20cm and a distance of 15cm15cm between them.
Given the length of parallel sides 24cm and 20cm, and the distance between parallel sides is 15cm.
We know that area of trapezium = ½ × (Sum of parallel sides) × Height
= ½ × (24+20) ×15cm2
= 22×15cm2 = 330cm2
Hence, the area of the given trapezium is 330cm²
Solved Examples
Example 1
The length and breadth of a wall are 20 ft. and 15 ft. respectively. The owner wants to get it covered with wallpaper. The price of the wallpaper is ₹50 per sq. ft. Find the Cost of covering the wall with the wallpaper?
Solution:
Area of the wall = l × b
= 20 × 15
= 300 sq. ft.
Cost of wallpaper = Area of the wall × Cost per sq. ft.
= 300 × 50
= ₹ 15000
Example 2
Calculate the area of a triangle with a 25m base and a 14m height.
Solution:
Here, base =25cm and Height =14cm
Area of a triangle = (1/2 ×base × height) sq. units
= (1/2×25×14) cm2
= 175cm2
Therefore, the area of the given triangle is 175cm2.
Example 3
Find the volume of a cube whose edge measures 8cm.
Solution:
Given, edge a=8cm,
we know that volume of a cube =a3 cubic units
= 83= 8×8×8cm3 = 512cm3
Hence, the volume of the given cube is 512cm3
Example 4
Calculate the circumference of a circle with a radius of 10.5cm
Solution:
Here, r=10.5 = 105/10= 21/2cm
we know that circumference of a circle =2πr
=2 × 22/7 × 21/2 cm
= 66 cm
Therefore, the circumference of a given circle is 66cm.
FAQs (Frequently Asked Questions)
You will find all geometry formulas on Extramarks.
The volume of a cube is √3a units.
You can memorise the formulas with constant practice and revision.