# 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