Geometry Formulas - Area, Solved Examples
Sawat Sayyed10 Sept, 2023
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Geometry Formulas : Geometry formulas play a crucial role in calculating various attributes such as dimensions, perimeter, area, surface area, and volume for different geometric shapes. Geometry is a branch of mathematics dedicated to understanding the relationships between points, lines, angles, surfaces, measurements, and properties of objects. This discipline is divided into two categories: 2D, which encompasses plane geometry, and 3D, which involves solid geometry.
2D shapes consist of flat figures possessing only two dimensions—length and width. Examples include squares, circles, and triangles. Conversely, 3D objects are solid entities with three dimensions—length, width, and height or depth. Examples comprise cubes, cuboids, spheres, cylinders, and cones.
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Geometry formulas are employed to calculate dimensions, perimeter, area, surface area, volume, and other attributes of both 2D and 3D geometric shapes. 2D shapes encompass flat figures such as squares, circles, and triangles. On the other hand, examples of 3D shapes include cubes, cuboids, spheres, cylinders, and cones. The fundamental geometry formulas are outlined below:
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Basic Geometry Formulas
Presented below are a range of 2D geometry formulas pertaining to distinct geometric shapes, accompanied by select formulas integrating the mathematical constant π (pi).
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Formulas for 2D Geometry:
- Perimeter of a Square = 4 × Side
- Perimeter of a Rectangle = 2 × (Length + Breadth)
- Area of a Square = Side²
- Area of a Rectangle = Length × Breadth
- Area of a Triangle = ½ × Base × Height
- Area of a Trapezoid = ½ × (Base ₁ + Base ₂ ) × Height
- Area of a Circle = A = π × r²
- Circumference of a Circle = 2πr
Moving on to the realm of 3D geometry, the fundamental formulas are enumerated below, featuring the incorporation of the mathematical constant π.
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- Curved Surface Area of a Cylinder = 2πrh
- Total Surface Area of a Cylinder = 2πr(r + h)
- Volume of a Cylinder = V = πr²h
- 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
- Surface Area of a Sphere = S = 4πr²
- Volume of a Sphere = V = 4/3 × πr³
Herein,
r denotes Radius,
h signifies Height, and
l represents Slant height.
Download PDF Geometry Formulas
The provided table showcases formulas for both 2D and 3D geometry.
| SHAPES | FORMULAS |
|---|---|
| 1. Right Triangle | Pythagoras Theorem: base 2 + height 2 = hypotenuse 2 Area = ½ × base × height Perimeter = base + height + hypotenuse |
| 2. Triangle | Perimeter, P = a + b + c Where, a, b, and c are the sides of a triangle. Area, A = ½ base × height |
| 3. Rectangle | Perimeter = 2(l + w) Area = lw Diagonal, d = √(l 2 + w 2 ) Where, l = length of a rectangle w = width of a rectangle |
| 4. Parallelogram | Perimeter, P = 2(a + b) Where, a and b are the sides of a parallelogram Area of parallelogram, A = base × height Height, h = Area/base Base, b = Area/height |
| 5. Trapezium | Area, A = ½(a + b)h Where, a and b are the parallel sides h = distance between two parallel sides |
| 6. Circle | Circumference = 2πr Area = πr 2 Diameter = 2r Where, r = radius of a circle |
| 7. Square | Perimeter, P = 4a Area, A = a 2 Diagonal, d = a√2 Side, a = √A Where, a = side of a square |
| 8. Arc | Arc Length, L = rθ Here, θ is the central angle in radians and r = radius |
| 9. Cube | Area, A = 6a 2 Volume, V = a 3 Edge, a = Volume ⅓ Space diagonal = a√3 Where, a = side of a cube |
| 10. Cuboid | Surface Area, A = 2(lb + bh + hl) Volume, V = lbh Space diagonal, d = √( l 2 + b 2 +h 2 ) Where, l= length b= breadth h= height |
| 11. Cylinder | Total Surface Area, A = 2πrh + 2πr 2 Curved Surface Area, Ac = 2πrh Volume, V = πr 2 h Base Area, Ab = πr 2 Radius, r = √(V/πh) Where, r= radius of a cylinder h= height of a cylinder |
| 12. Cone | Total Surface Area, A = πr(r+l) = πr[r+√(h 2 +r 2 )] Curved Surface Area, A c = πrl Volume, V = ⅓πr 2 h Slant Height, l = √(h 2 +r 2 ) Base Area, A b = πr 2 Where, r= radius of a cone h= height of a cone l = slant height |
| 13. Sphere | Surface Area, A = 4πr 2 Volume, V = ⁴⁄₃πr 3 Diameter = 2r Where, r= radius of a sphere |
Geometry Formula FAQs
Q1. What are the formulas for the geometric properties of a cuboid?
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What is the formula of the circle?
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