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Parin Sir > Quantitative Aptitude (Maths) > Mensuration > Mensuration

Mensuration

August 9, 2020
Category: Mensuration

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☼ Plane Diagrams : –

■ Triangle :–

■ Triangle :–

Perimeter ( 2s )

= a + b + c

$\therefore$ Semi – perimeter ( s )

= $\frac{\mathrm{a\ }+\mathrm{\ b\ }+\mathrm{\ c}}{2}$

Area ( \Delta )

= $\frac{1}{2}$ Base $\times$ Altitude

= $\sqrt{s(s-a)(s-b)(s-c)}$

= $\frac{1}{2}$ bc sin A

= $\frac{1}{2}$ ab sin C

= $\frac{1}{2}$ ac sin B

■ Equilateral Triangle :–

Perimeter = x + x + x

= 3 x

Area = $\frac{\sqrt3}{4}\ x^{2}\$

= $\frac{h^2}{\sqrt3}$

■ Parallelogram

Perimeter = AB + BC + CD + DA

Area = Base $\times\$ Height

= b h

■ Rectangle

Perimeter = l + b + l + b

= 2 l + 2b

= 2 (l + b )

Area = l b

■ Rhombus

Perimeter

= AB + BC + CD + DA

= 4 AB

Area

= b h

or

= $\frac{1}{2}AC \times BD$

■ Square

Perimeter = l + l + l + l

= 4 l

Area = l²

= AC²

■ Trapezium

Perimeter

= AB + BC + CD + DA

Area

= h

Perimeter

= AB + BC + CD + DA Area

= $\left(\frac{\mathrm{AB\ }+\mathrm{\ CD}}{2}\right)\times$ h

■ Circle

Circumference = 2 π r

Area = π r²

■ Minor Arc

Length of Arc ( l ) = $\frac{\mathrm{\pi\ r\ \theta}}{\mathrm{18}\mathrm{0}^\mathrm{0}}$

■ Major Arc

Length of Arc ( l ) = 2π r – $\frac{\pi\ r\ \theta}{180^0}$

■ Minor Sector

Area = $\frac{\pi\ r^2\theta}{360^0}$

= $\frac{1}{2} l r$

( Where, l = length of the minor arc )

■ Major Sector

Area = $\pi$ r² – $\frac{\pi\ r^2\theta}{360^0}$

= $\frac{1}{2} l r$

( Where, l = length of the major arc )

■ Minor Segment

Area = Area of Minor Sector – Area of Triangle

= $\frac{\pi\ r^2\theta}{360^0}$ – Area of Triangle.

■ Major Segment

Area = Area of Major Sector + Area of Triangle

= Area of Circle ( $\pi$ r²) – Area of Minor Segment

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