## Formulas for Areas and Volumes

**Circle:**

- Diameter, D = 2R
- Area = πR
^{2}sq. units - Circumference = 2πR units

**Square:**

- Area = a
^{2}sq. units - Perimeter = 4a units
- Diagonal, d = √2 a units

**Rectangle:**

- Area = L*B sq. units
- Perimeter = 2(L+B) units
- Diagonal, d = √L
^{2}+B^{2}units

**Right Angled Triangle:**

- Area = (½)bxh sq. units
- Perimeter = b + h + hypotenuse
- Hypotenuse = √b
^{2}+h^{2}units

**Equilateral Triangle:**

- Area = √4 a
^{2}sq. units - Perimeter = 3a units, where a = side of the triangle

**Scalene Triangle:**

- Area: √s(s-a)(s-b)(s-c) sq. units; s = (a+b+c)/2
- Perimeter = (a+b+c) units

**Isosceles Triangle:**

- Area = b/4 √4a
^{2}-B^{2}sq units - Perimeter = 2a + b units, where b = base length; a = equal side length

**Cube:**

- Volume = a
^{3}cubic units - Lateral Surface Area (LSA) = 4a
^{2}sq. units - Total surface area (TSA) = 6a
^{2}sq. units - Length of diagonal = a√3 units

**Cuboid:**

- Volume = (Cross section area * height) = L * B * H cubic units
- Lateral Surface Area (LSA) = 2[(L+B)H] sq. units
- Total surface area (TSA) = 2(LB+BH+HL) sq. units
- Length of the diagonals = √L
^{2}+B^{2}+H^{2}units

**Sphere:**

- Volume = (4/3) πR
^{3}cubic units - Surface Area = 4πR
^{2}sq. units - If R and r are the external and internal radii of a spherical shell, then its Volume = (4/3) [R
^{3}-r^{3}] cubic units

**Hemisphere:**

- Volume = (2/3) πR
^{3}cubic units - TSA = 3πR
^{2}sq. units

**Cylinder:**

- Volume = πr
^{2}h cubic units - Curved surface Area (CSA) (excludes the areas of the top and bottom circular regions) = 2πRh sq. units
- TSA = Curved Surface Area + Areas of the top and bottom circular regions = 2πRh + 2πR
^{2}= 2πR[R+h] sq. units

**Cone:**

- Volume = (1/3) πR
^{2}h cubic units - Slant Height of cone, L = √R
^{2}+H^{2}units - CSA = πRL sq. units

### Other shapes

- Area of a parallelogram = (base x height)
- Area of a rhombus= 1/2(product of diagonals)
- Area of a trapezium= 1/2 (sum of parallel sides) x (distance between them)