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Geometry, often regarded as one of the oldest branches of mathematics, delves into the intricate study of shapes, figures, surfaces, and solids. At the heart of mastering geometry lies a deep understanding of its formulas, which play a pivotal role in unraveling the properties and dimensions of various geometric entities. In this article, we embark on a journey through the realm of geometry, exploring a comprehensive list of formulas accompanied by solved examples.
Understanding Geometry Formulas
Geometry formulas serve as indispensable tools for calculating essential attributes such as perimeters, areas, volumes, and surface areas of both 2-dimensional and 3-dimensional figures. Whether you’re dealing with triangles, rectangles, circles, or more complex shapes, these formulas provide a systematic approach to solving geometric problems.
List of Geometry Formulas
1. Triangle:
- Area = ½ x base x perpendicular
- Perimeter = Sum of all sides
2. Rectangle:
- Area = Length x Breadth
- Perimeter = 2 (Length + Breadth)
- Diagonal (d) = √ ((length)² + (breadth)²)
3. Square:
- Area = side x side
- Perimeter = 4 x Side
- Diagonal (d) = side x √2
4. Circle:
- Area = π x r x r
- Circumference = 2 x π x r
- Diameter = 2r
5. Trapezium:
- Perimeter = Sum of all sides
- Area = ½ x sum of parallel sides x distance between parallel sides
6. Parallelogram:
- Perimeter = Sum of all sides
- Area = base x height
7. Cube:
- Surface Area = 6 x (side)²
- Volume = (side)³
8. Cuboid:
- Surface Area = 2(lb + bh + hl)
- Volume = l x b x h
9. Sphere:
- Surface Area = 4 x π x r²
- Volume = 4/3 x π x r³
- Diameter = 2r
10. Cone:
- Base Area = πr²
- Total Surface Area = πr (r + l)
- Volume = 1/3πr²h
- Slant height (l) = √ (h² + r²)
11. Cylinder:
- Total Surface Area = 2πr (r + h)
- Curved Surface Area = 2πrh
- Volume = πr²h
- Base Area = πr²
Solved Examples
Example 1:
Find the area and perimeter of a rectangle with a length of 5 cm and breadth of 8 cm.
- Area = Length x Breadth = 5cm x 8cm = 40 cm²
- Perimeter = 2 (Length + Breadth) = 2 (5 + 8) = 26 cm
Example 2:
Calculate the curved surface area of a cylinder with a height of 14 cm and a radius of 10 cm.
- Lateral Surface Area = 2πrh = 2 x 22/7 x 10 x 14 = 880 cm²
Example 3:
Determine the volume of a cone with a slant height of 9 cm and a radius of the base of 4 cm.
- Slant height (l) = √ (h² + r²) → h = √65 → h = 8.06 cm
- Volume = 1/3πr²h = 133.62 cm³
Example 4:
Find the surface area of a cubical water tank with a side length of 1.5 m.
- Total Surface area = 6 (side)² = 13.50 m²
Read Also: Surface Area And Volume Formulas PDF
In this journey through geometry formulas, we’ve not only explored the fundamental equations but also applied them to real-world problems. Armed with this knowledge, you’re now equipped to navigate the intricate world of geometry with confidence and precision.