SOME IMPORTANT FORMULAS RELATED TO MENSURATION

 SOME IMPORTANT FORMULAS RELATED TO MENSURATION

Right Angled Triangle

It is one whose one of the angles is right angle , i.e., 90°.

1. (Hypotenuse)² = (Perpendicular)² + (Base)²

2. Area = 1÷2*Base*Perpendicular

EQUILATERAL TRIANGLE

All sides are equal in length and all three angles are equal to 60°.

1. Area = √3÷4*(Side)²

2. Area = (Height)²÷√3

3. Height = √3÷2*Side

4. Perimeter = 3*side

ISOSCELES TRIANGLE

Two sides are equal in lengths.

1. Area = b÷4√4a²-b²

where , a = lengths of equal sides b = length of unequal side.

2. In an isosceles right triangle , 

(a) Hypotenuse = √2*congruent side(a)

(b) Area = 1÷2*a²

(c) Perimeter = √2*a(√2+1)

RECTANGLE

1. Area = length(l)* breadth (b)

2. Perimeter = 2(l+b)

3. Diagonal = √l²+b²

SQUARE

1. Area = (Side)²

2. Perimeter = 4*Side

3. Diagonal = Side*√2

PARALLELOGRAM

In parallelogram opposite sides are parall and equal.

The two diagonals are not always equal but they bisect each other at the point of intersection.

Area = Base* Height.

TRAPEZIUM

It is a quadrilateral whose one pair of opposite sides is parallel. Other two sides are oblique.

Area = 1÷2*Height*(Sum of parallel sides)

Here , height is the distance between the two parallel sides.

RHOMBUS

It is a parallelogram whose all sides are equal and diagonals bisect each other at right angles.

1. Area = 1÷2*Product of diagonals.

2. Side = √(d1÷2)²+(d2÷2)² , where d1 and de are diagonals

3. Perimeter = 4* side

QUADRILATERAL

Area = 1÷2*one diagonal *(sum of perpendicular to it from opposite vertices) = 1÷2*d*(a+b)

CIRCLE

1. Diameter = 2*Radius

2. Area = πr² = π÷4*(d)2

where d = diameter = √4A÷π

3. Circumference = 2πr = πd

4. Radius = Circumference÷2π =√ Area÷π

POLYGON

1. Interior angle + Exterior angle = 180°

2. Each interior angle = (2n-4÷n)*90°

where n = number of sides.

3. Sum of Exterior angles = 360°

4. Perimeter = Number of sides * Length of side.

VOLUME AND SURFACE AREA

CUBOID

1. Volume = (Length (l)*Breadth (b)*Height (h))

2. Whole Surface Area =2(lb+bh+lh)

3. Diagonal = √l²+b²+h²

4. Area of 4 walls of a room = 2*h(l+b)

CUBE 

In a cube , Length = Breadth = Height.

1. Volume = (l)³

2. Length = ³√Volume

3. Whole Surface Area = 6 l²

4. Diagonal = l*√3

5. Lateral Surface Area = 4 l²

CYLINDER

1. Volume = πr²h

2. Curved Surface Area = 2πrh

3. Total Surface Area = 2πr(r+h)

where r = radius , h= height

SPHERICAL CELL

1. Volume = 4÷3π(R³-r³)

2. Total Surface Area = 4π(R²-r²)

where , R = Outer radius , r = Inner radius.

SPHERE

1. Volume = 4÷3πr³

2. Surface Area = 4πr²

SEMI-SPHERE

1. Volume = 2÷3πr³

2. Curved Surface Area = 2πr²

3. Total Surface Area = 3πr²

CONE

1. Slant height (l) = √r²+h²

2. Volume = 1÷3πr²h

3. Curved Surface Area = πr²l

4. Total Surface Area = πr (l+r)

5. If the depth of the frustum of a cone be k and radii of its ends are r1 and r2, then

(1) Slant height of the frustum of the cone = √k²+(r1-r2)²

(2) Curved surface area of the frustum = π(r1+r2) l.

(3) Volume = πk÷3(r1²+rate+r2²)