Area and Perimeter of Shapes Tricks and Formulas

Pythagoras Theorem

For right triangle ABC

Right Triangle ABC

Right Triangle ABC

Right Triangle ABC

AC2=AB2+BC2

For acute triangle ABC

Acute Triangle ABC

Acute Triangle ABC

Acute Triangle ABC

AC2=AB2+BC22×BC×BD

For obtuse triangle ABC

Obtuse Triangle ABC

Obtuse Triangle ABC

Obtuse Triangle ABC

AC2=AB2+BC2+2×BC×BD

Area of Triangle

When lengths of the sides are given

When lengths of the sides are given

When Lengths of the Sides Are Given

When lengths of the sides are given

Area=s(sa)(sb)(sc)

Where,semiperimeter(S)=a+b+c2

When lengths of the base and altitude are given

When lengths of the base and altitude are given

When Lengths of the Base and Altitude Are Given

When lengths of the base and altitude are given

Area=12bh

When lengths of two sides and the included angle are given

When lengths of two sides and the included angle are given

When Lengths of Two Sides and the Included Angle Are Given

When lengths of two sides and the included angle are given

Area=12absinθ

For Equilateral Triangle

Are of Equilateral Triangle

Equilateral Triangle

Are of Equilateral Triangle

Area=34a2

For Isosceles Triangle

Area of Isosceles Triangle

Isosceles Triangle

Area of Isosceles Triangle

Area=b4×4a2b2

Apollos Theorem

Apollus Theorem

Apollus Theorem

Apollus Theorem

If AD is the median, then:

AB2+AC2=2(AD2+BD2)

Angle Bisector Theorem

Angle Bisector Theorem

Angle Bisector Theorem

Angle Bisector Theorem

If AD is the angle bisector for angle A, then:

ABBD=ACCD

Area of Quadrilateral

For Cyclic Quadrilateral

Area=(sa)(sb)(sc)(sd)

where,semiperimeter(s)=a+b+c+d2

If lengths of one diagonal and two offsets are given

If lengths of one diagonal and two offsets are given

If Lengths of One Diagonal and Two Offsets Are Given

If lengths of one diagonal and two offsets are given

Area=12d(h1+h2)

If lengths of two diagonals and the included angle are given

If lengths of two diagonals and the included angle are given

If Lengths of Two Diagonals and the Included Angle Are Given

If lengths of two diagonals and the included angle are given

Area=12d1d2sinθ

For Trapezium

 Area of Trapezium

Trapezium

Area of Trapezium

Area=12(b1+b2)h

For Parallelogram

Area of Parallelogram

Parallelogram

Area of Parallelogram

Area=bh

For Rhombus

Area of Rhombus

Rhombus

Area of Rhombus

Area=12d1d2

The halves of diagonals and a side of a rhombus form a right angled triangle with side as the hypotenuse.

For Rectangle

Area of Rectangle

Rectangle

Area of Rectangle

Area=lb

Perimeter of a rectangle =2(length+breadth)

For Square

Area of Square

Square

Area of Square

Area=A2

Area of a square =½(diagonal)2

Area of 4 walls of a room =2(length+breadth)×height

Polygons

Number of Diagonals

Nd=n(n3)2

The sum of all the interior angles

Ai=(n2)1800

The sum of all the exterior angles

Ae=3600

Area of Regular Hexagon

Area of Regular Hexagon

Regular Hexagon

Area of Regular Hexagon

Area= 332a2

Circle

Area of Circle

Circle

Area of Circle

Circumference

c=2πr

Area

A=πr2

Length of Arc

l=2πr(θ3600)

Area of Sector

As=πr2(θ3600)

Or

As=12lr

Perimeter of Sector

Ps=l+2r

Ellipse

Area of Ellipse

Ellipse

Area of Ellipse

If semi-major axis (OD)=a and semi-minor axis (OA)=b,

Perimeter of the ellipse

Pe=π(a+b)

Area of the ellipse

Ae=πab