QUANTITATIVE APTITUDE

Mensuration

• Area = ½ (a x h1) = ½(b x h2) = ½(c x h3)

• Semi-Perimeter s = (a + b + c)/2• Area = √(s x (s – a) x (s - b) x (s - c))• Perimeter = a + b + c

TRIANGLE

EQUILATERAL TRIANGLE(Sides a)

• Area = √3/4 x a2

• Perimeter = 3 x a• Height = √3/2 x a

TRIANGLE(Sides a, b, c; Opp. Angles A, B, C respectively; heights h1, h2 and h3 respectively)

a a

a

A

B C

A

aB

b

h1

h2

h3

c

C

RECTANGLE & SQUARERECTANGLE(length l; breadth b)

• Area = l x b• Perimeter = 2(l + b)

SQUARE(side a)

• Area = a2

• Perimeter = 4a

l

b

a

a

PARALLELOGRAM & RHOMBUSPARALLELOGRAM(height h, base b, other side a)

• Area = b x h• Perimeter = 2 x (a + b)

• Area = ½ (d1 x d2)• Perimeter = 4 x a

h d1d2

b

a

a

RHOMBUS(side a; diagonals of length d1 and d2 )

a

TRAPEZIUM & KITE

• Area = ½ (a + b) x h• Perimeter = a + b + c + d

• Area = ½ (d1 x d2)• Perimeter = a + b + c + d

a

b

h

d1

d2

TRAPEZIUM(distance between parallel sides h, length of parallel sides a & b)

KITE(diagonals of length d1 and d2 )

c d

dc

b a

• Area = πr2/2• Perimeter= πr + 2r

CIRCLE & SEMI-CIRCLE

• Area = πr2

• Circumference = 2πr

rrO

O

CIRCLE(radius r)

SEMI-CIRCLE(radius r)

• Area = /360 x (πr2)• Length of arc = (/360 x 2πr ) • Perimeter = (/360 x 2πr ) + 2r

SECTOR AND SEGMENT OF CIRCLESECTOR(centre O, radius r, angle of sector )

SEGMENT (centre O, radius r, angle of sector )

• Area = 1/2r2 x {(/180) x π –Sin }

r

O

r

O

CUBE AND CUBOID

• Volume = a3

• Total Surface Area = 6a2

• Longest diagonal = a x √3

• Volume = l x b x h• Total Surface Area = 2{(l x b) + (b x h) + (l x

h)}• Longest diagonal = √(l2 + b2 + h2)

a

a

a

lb

h

CUBE(length = breadth = height = a)

CUBOID(length l; breadth b; height h)

• Volume = π x r2 x h• Total Surface Area = 2π x r x (h + r)• Curved (Lateral) Surface Area = 2π x r x h

• Volume = 1/3 π x r2 x h• Total Surface Area = π x r x (l + r)• Curved (Lateral) Surface Area = π x r x l

CYLINDER AND CONE

r

r

hh

r

l

CYLINDER (height h; radius of base r)

CONE(height h; radius of base r; slant height l )

• Volume = 4/3 π x r3

• Total Surface Area = 4π x r2

HEMISPHERE AND SPHERE

• Volume = 2/3 π x r3

• Total Surface Area = 3π x r2

• Curved (Lateral) Surface Area = 2π x r2

rr

HEMISPHERE(radius r)

SPHERE(radius r)

PRISM(length of side of base a; number of sides of base n; height h)

• For a right prism, base can be any shape like square, triangle, pentagon or hexagon as shown

• Volume = area of base x h• Total Surface Area = 2 x area of base + n x

(h x a)• Lateral surface area = n x (a x h)

PYRAMID(length of side of base a; number of sides of base n; height h; slant height l)

• For a right pyramid, base can be any shape like square, triangle, pentagon or hexagon as shown

• Volume = 1/3 x area of base x h• Lateral surface area = ½ x (n x a) x l• Total Surface Area = area of base + lateral

surface area

ha

l

n = 6 for hexagon

a

n = 6 for hexagon

h

PYRAMID & PRISM

FRUSTUM OF CONESlant height l; height h, radius of small base r; radius of large base R

• Volume = 1/3π x h (R2 + r2 + Rr)• Total Surface Area = π x (R2 + r2 + Rl +

rl)• Lateral Surface Area = π x l (R + r)• Slant height l = √{(R-r)2 + h2}

FRUSTUM OF PYRAMIDSlant height l; height h, side of base a

• Volume = 1/3 x h x (A1 + A2 + √A1A2)

• Lateral Surface Area = ½ x perimeter of base x l

• Total Surface Area = LSA + A1 + A2

FRUSTUM OF CONE AND PYRAMID

h l

R

rl

A2 a

h

A1

Thank You

Kaushal