# 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

Area =

Perimeter = p + b + h

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

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 =

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