# List of Geometry Formulas

Sub Topics

### Geometry:

Geometry is the part of mathematics. Geometry is the study of shape, size in 2-dimensional and 3-dimensional.

Formulas for 2-Dimensinal

Area of geometrical figure

1. Rectangle area= l $\times$ w
Where l=length and w=width

2. Square area= s2
Where s= side

3. Triangle area=1/2 b $\times$ h
Where b= base and h=height

4. Trapezoid area=1/2 h(b1+b2)
Where h=height and  b1,b2= bases

5. Circle area= $\pi$ $\times$ r2

6. Sector of circle area=1/2 $\theta$*r2

7. Ellipse area=$\pi$ $\times$ a $\times$ b
Where a = semimajor axis and b= semiminor axis

8. Parallelogram area=b $\times$ h
Where b=base and h=height

9. Annulus area=$\pi$(R2-r2)

Perimeter of Geometrical Figure

1. Rectangle, P = 2l + 2w
Where l = length and w = width

2. Square, P = 4s
Where s = side

3. Triangle, P = a + b + c
Where a,b,c are side

4. Trapezoid, P = a + b + c + d
Where a,b,c and d are side

5. Parallelogram, P = 2a + 2b
Where a and b are side

Circumference of geometrical figure

1. Ciircle, C = 2$\pi$ $\times$ r

2.  Ellipse, C= $\pi$(3(a + b)) - √[(a + 3b)(b + 3a)]
Where a = semimajor axis and b = semiminor axis

## Formulas for 3-Dimensinal

Surface area of geometrical figure

1. Cube, S = 6s2
Where s=side

2. Rectangular solid, S = 2lw + 2lh + 2wh
Where l = length ,w = width and h = height

3. Sphere, S=4$\pi$ $\times$ r2

4. Right circular cylinder, S=2$\pi$ $\times$ r $\times$ h + 2$\pi$ $\times$ r2
Where r = radius and h = height

5. Torus, S=4$\pi2$ $\times$ r $\times$ R

6. Right circular cone, S=$\pi$ $\times$ r(√(h2+r2)+r)

Volume of geometrical figure

1. Cube, V=s3
Where s = side

2. Rectangular solid, V = l $\times$ w $\times$ h
Where l=length ,w= width and h=height

3. Sphere, V=4/3 $\pi$ $\times$ r3

4. Right circular cylinder, V=$\pi$ $\times$ r2 $\times$ h

5. Torus, V=2$\pi2$ $\times$ r2 $\times$ R

6. Right circular cone, V=1/3 $\times$ $\pi$ $\times$ r2 $\times$ h

## Uses of Formulas

Formulas are used to figure out the answers in a quicker way.

Example 1:

A water tank is of length 120cm, width 100cm and height 80cm.What is the Volume of the tank?

Solution:

We are asked to find the volume of tank for the given length, width and height.
The tank is in the shape of a Rectangular.

For finding the answer, we make use of the formula.

V = L × W × H

V = 120cm x 100cm x 80cm

V = 960000 cubic cm

Example 2:

A park is of length 250 meters and width 220 meters.

What is the perimeter of the park?

Solution:

Here, we need to find the perimeter of the park.

The park is in the shape of rectangle.

So, the answer can be found easily by using the formula.

P = 2 (L + W)

P = 2 (250m + 220m)

P = 2 (470m)

P = 940m