# Important Mensuration Formulas-Area & Perimeter

## Area and perimeter

### TRIANGLE

1. __Equilateral Triangle__

Area

Height (h)

Perimeter = 3a

2. __Isosceles Triangle__

Area

h =

Perimeter= 2a+b

3. __Scalene triangle__

Area = Where S =

Perimeter = a + b + c

4. Right angled Triangle

Perimeter = p + b + h

*Note*: Side of the maximum size square inscribed in a right-angle triangle.

### QUADRILATERAL

1. Parallelogram

Area = Base Height = b h

Perimeter = 2(a + b)

2. Trapezium

Area = ( Sum of Parallel Sides Height) = (a + b) h

Perimeter = a + b+ c+ d

3. Rhombus

Area = d1 d2

a =

Perimeter = 4a

=

4. Rectangle

Area = l b

Perimeter = 2 (l + b)

d =

5. Square

Area =

Perimeter = 4a

Diagonal (d) =

### REGULAR POLYGON

- Each Exterior angle =
- Each Interior angle =
- Number of Diagonals= or,
- Sum of Exterior angle =
- Sum of Interior angle = (n-2)
- Sum of interior and Exterior =

### CIRCLE

Area =

Circumference =

Diameter= 2r

Length of arc (*l*) =

Area of Sector =

Perimeter of Sector = + 2r

**For Circular Ring**

Area =

### SEGMENT

Area = area of sector OACB – area of ∆OAB =

Perimeter = length of ARC ACB + Chord length AB = (2πr)

AB = 2r sin

### IMPORTANT POINTS TO BE REMEMBER

- If the length and breadth of a rectangle are increased by a% and b% respectably, then area will be increased by
- If all the increasing sides of any two dimensional figure are changed by a%, then the area will be changed by

In case of circle, radius (or diameter) is increased in place of sides.

- If all the measuring sides of any two-dimensional figure are changed by a% , then its perimeter also changes by a%
- If area of a square is a square unit, then the area of the circle formed by the same perimeter is given by square unit.
- The area of the largest triangle inscribed in a semi circle of radius r =
- Area of square inscribed in a circle of radius r =