Geometry Formulas

Basic Geometry Formulas

Geometric shapes

PerimeterofaSquare=P=4a

Where a = Length of the sides of a Square

PerimeterofaRectangle=P=2(l+b)

Where, l = Length ; b = Breadth

AreaofaSquare=A=a2

Where a = Length of the sides of a Square

AreaofaRectangle=A=l×b

Where, l = Length ; b = Breadth

AreaofaTriangle=A=b×h2

Where, b = base of the triangle ; h = height of the triangle

AreaofaTrapezoid=A=(b1+b2)h2

Where, b1 & b2 are the bases of the Trapezoid ; h = height of the Trapezoid

AreaofaCircle=A=π×r2

CircumferenceofaCircle=A=2πr

Where, r = Radius of the Circle

SurfaceAreaofaCube=S=6a2

Where, a = Length of the sides of a Cube

SurfaceAreaofaCylinder=S=2πrh

VolumeofaCylinder=V=πr2h

Where, r = Radius of the base of the Cylinder ; h = Height of the Cylinder

SurfaceAreaofaCone=S=πr(r+h2+r2−−−−−−√)

VolumeofaCone=V=πr2h

Where, r = Radius of the base of the Cone, h = Height of the Cone

SurfaceAreaofaSphere=S=4πr2

VolumeofaSphere=V=43πr3

Where, r = Radius of the Sphere

Angle Formula

Angle is formed when two rays intersect i.e. half-lines projected with a common endpoint. The corner points of angle is known as the vertex of the angle and the rays as the sides, i.e. the lines are known as the arms. It is defined as the measure of turn between the two lines. The unit of angle is radians or degrees. There are different types of formulas for angles some of them are double-angle formula, half angle formula, compound angle formula, interior angle formula etc.

Central Angle Formula = 

Angle=ArcLength×3602πRadius

Formula for Central Angle

s=rθ

Where, s represents the arc length,
S = rθ represents the central angle in radians and r is the length of the radius.

Formula for Double Angle

cos(2a)=cos2(a)–sin2(a)=2cos2(a)−1=1−2sin2(a)

sin(2a)=2sin(a)cos(a)

tan(2a)=2tan(a)1−tan2(a)