Common Area and Volume Formula

2D Shapes (Area)

1. Square

   • Area: $A = a^2$ (where $a$ is the side length)

2. Rectangle

   • Area: $A = l \times w$  (where $l$ is length and $w$ is width)

3. Triangle

   • Area: $A = \frac{1}{2} b \times h$ (where $b$ is base and $h$ is height)

4. Circle

   • Area: $A = \pi r^2$ (where $r$ is the radius)

5. Trapezium (Trapezoid)

   • Area: $A = \frac{1}{2} (a + b) \times h$ (where $a$ and $b$ are the parallel sides, and $h$ is the height)

6. Parallelogram

   • Area: $A=b\times \mathrm{h (where }$$b$ is base and $h$ is height)

3D Shapes (Surface Area and Volume)

1. Cube

• Surface Area: $SA = 6a^2$ (where $a$ is the side length)
• Volume: $V = a^3$
  

2. Rectangular Prism (Cuboid)

• Surface Area: $SA = 2(lw + lh + wh)$
  
• Volume: $V = l \times w \times h$
  

3. Sphere

• Surface Area: $SA=4\pi r^2$
• Volume: $V = \frac{4}{3} \pi r^3$
  

4. Cylinder

• Surface Area: $SA = 2\pi r (r + h)$ (where $r$ is the radius, $h$ is the height)
• Volume: $V = \pi r^2 h$
  

5. Cone

• Surface Area: $SA = \pi r (r + l)$ (where $l = \sqrt{r^2 + h^2}$ is the slant height)
• Volume: $V=\frac{1}{3}\pi r^{2}h$

6. Pyramid (Square Base)

• Surface Area: $SA = b^2 + 2b \cdot l$ (where $l = \sqrt{\frac{b^2}{4} + h^2}$)
• Volume: $V = \frac{1}{3} b^2 h$
  

7. Rectangular Pyramid

• Surface Area: $SA = lw + l\sqrt{\left(\frac{w}{2}\right)^2 + h^2} + w\sqrt{\left(\frac{l}{2}\right)^2 + h^2}$
• Volume: $V = \frac{1}{3} l \times w \times h$
  

8. Torus

• Surface Area: $SA = 4\pi^2 Rr$ (where $R$ is the major radius, $r$ is the minor radius)
• Volume: $V = 2\pi^2 Rr^2$
  

9. Hemisphere

• Surface Area: $SA = 3\pi r^2$ (including the base)
• Volume: $V = \frac{2}{3} \pi r^3$