Mensuration for CTET Exam

Plan figures

Figures Perimeter Area Image
Triangle = a + b + c \sqrt{s(s-a)(s-b)(s-c)}

Where s = \frac{a+b+c}{2}

 

\frac{1}{2}\: bh

Right angled triangle a+b+\sqrt{a^{2}+b^{2}} \frac{1}{2}\: ab
Equilateral triangle 3a \frac{\sqrt{3}}{4}\: a^{2}
Isosceles triangle 2a + b \frac{b}{4}\sqrt{4a^{2}-b^{2}}
Circle 2\pi r \pi r^{2}
Sector of a circle \frac{\theta}{360}\times2\pi r+2r(\theta is in degrees) \frac{\theta }{360}\times \pi r^{2}
Square 4a a^{2}
Rectangle 2(l + b) lb
Trapezium a + b + c + d \frac{1}{2}(a+b)h
Parallelogram 2(a + b) bh or ab sin\theta
Cyclic quadrilateral a + b + c + d \sqrt{(s-a)(s-b)(s-c)(s-d)} 

S =  \frac{a+b+c+d}{2}

Rhombus 4a  \frac{1}{2}\times product\:of\:diagonal
Ring  2\pi (R+r)  \pi R^{2}-\pi r^{2}

Solids

Figure Lateral Surface Area Total Surface Area Volume Images
Cube  4a^{2}  6a^{2}  a^{3}
Cuboid 2h(l + b) 2(lb + bh + lh) lbh
Cylinder  2\pi rh  2\pi r(r+h)  \pi r^{2}h
Cone  \pi rl  \pi r(l+r)  \frac{1}{3}\pi r^{2}h
Sphere  4\pi r^{2}  \frac{4}{3}\pi r^{3}
Hemisphere  2\pi r^{2}  3\pi r^{2}  \frac{2}{3}\pi r^{3}

Important Questions for Mensuration

Mensuration

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