Mensuration is the branch of mathematics which studies the measurement of the 2D and 3D figures on parameters like length, volume, shape, surface area etc. Objects or quantities can be measured using both standard and nonstandard units of measurement.

Important Formulas 

Rectangle 

Area = lb

Perimeter  = 2(l+b)

Square 

Area = a×a

Perimeter = 4a

Parallelogram 

Area = l × h

Perimeter = 2(l+b)

Triangle 

Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….

where s=a+b+c/2

Right angle Triangle 

Area =1/2(bh)

Perimeter = b+h+d

Equilateral Triangle 

Area = √3. a²/4 or  ½(ah)….where h = √3/2

Perimeter = 3a

Circle 

Area =  πr^2 or πd^2/4

Circumference = 2πr  or πd

Area of sector of a circle = (θπr^2 )/360

Right Circular Cylinder 

Volume of Cylinder = π r² h

Lateral Surface Area (LSA or CSA) = 2π r h

Total Surface Area = TSA = 2 π r (r + h)

Volume of hollow cylinder = π r h(R² – r²)

Right Circular cone 

Volume = 1/3 π r²h

Curved surface area: CSA=  π r l

Total surface area = TSA = πr(r + l )

Sphere

Volume: V = 4/3 πr³

Surface Area: S = 4πr²

The height of an equilateral triangle is 4√3 cm. Find its perimeter.

a) 20 cm                       b) 24 cm                       c) 28 cm                       d) 30 cm

Solution:

Height of an equilateral triangle = (√3 / 2) × a     Þ        4√3 = (√3 / 2) × a    Þ   a = 8 cm

⸫ Perimeter of an equilateral triangle = 3a = 3 × 8 = 24 cm.

Answer: b

Q2. If the base of an isosceles triangle is 18 cm and length of equal sides is 15 cm, then what is the area?

a) 108 sq.cm.                b) 120 sq.cm.                c) 115 sq.cm.                d) 110 sq.cm.

Solution:

Area of isosceles triangle, A = (b / 4) × √(4a² – b²)

Here, base b = 18 cm, lengths of equal sides a = 15 cm 

Area, A = (18 / 4) × √(4 × 15² – 18²) = 108 sq.cm.

Answer: a

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