1. The document lists important mathematical formulas for calculating areas and perimeters of basic shapes like triangles, rectangles, squares, circles, cylinders, cones, spheres, pyramids and prisms. 2. It includes formulas to find the perimeter and area of triangles, rectangles, squares, circles, as well as surface areas of cubes, cylinders, cones, spheres and pyramids. 3. The formulas use variables like length, breadth, radius, height, base, and diagonals to calculate dimensions of the shapes.

1. Important Mathematical Formulas
Geometry
1. Pythagoras Formula : h2
= p2
+ b2
=> h = +
p2
= h2
– b2
=> p = √ −
b2
= h2
– p2
=> b = −
2. Perimeter of a triangle = sum of the length of its three sides
Perimeter of an equilateral triangle = 3 × sides
3. Perimeter of a rectangle = 2(length + breadth)
Length = – breadth
Breadth = – length
4. Perimeter of a square = 4 × side
Length of side =
5. Perimeter of a rhombus = 4 × side
Length of side =
6. Perimeter of a parallelogram = 2 ×(sum of two adjacent sides)
7. Circumference of a circle = 2 r
8. Perimeter of a semicircle = r( + 2)
9. Area of a triangle = × base × height
10. Area of a rectangle = length × breadth
Length = Breadth=
11. Area of a square = side × side
Side of a square = √
12. Area of a parallelogram = Base × Height
13. Area of a rhombus = × d1 × d2 [where, d1 and d2 are two diagonals]

2. 14. Area of a trapezium = × (a + b) × h [where, 'a' and 'b' are two parallel
sides and 'h' is height]
15. Area of a circle = r2
16. Lateral Surface Area of a cuboid = 2 × (l + b) × h
Total Surface Area of a cuboid = 2 × (lb + bh + lh)
Diagonal of a cuboid = √ + +
17. Lateral Surface Area of a cube = 4 × l2
Total Surface Area of a cube = 6 × l2
Diagonal of a cube = l√
18. Curved Surface Area of a solid cylinder = 2
Total Surface Area of a solid cylinder = 2 r2
+2
= 2 r (r + h)
Curved Surface Area of a hollow cylinder = 2 + 2 = 2 (R + r)
Surface Area of a hollow cylinder = 2 + 2 + 2( R2
– r2
)
Area of the ring = R2 –
r2
= (R2
– r2
)
Thickness of the ring = R – r
19. Curved Surface Area of a cone = [where, l = slant height]
Total Surface Area of a cone = r2
+ = r(r + l)
20. Surface Area of a sphere = 4 r2
Surface Area of a hemisphere = 3 r2
21. Surface Area of a prism = 2 × area of base + perimeter of base × height
22. Surface Area of any pyramid = area of base + area of each of lateral faces
23. Surface Area of regular pyramid = area of base + × ps
Where, p = perimeter of the base
s = slant height
24. Surface Area of square pyramid = b2
+ 2bs
[Where, b = length of the base, s = slant height]