Question

All the maths formulas for mensuration

Answer 1

Rectangle :
Area = $l\times b$
Perimeter = $2(l+b)$

Square :
Area = $a\times a$
Perimeter = $4a$

Parallelogram
Area = $l\times h$
Perimeter = $2(l+b)$

Triangle :
Area =$\frac{1}{2}\times b\times h$ or $\sqrt{s(s-a)(s-b)(s-c)}$,where $s=\frac{a+b+c}{2}$

Right angle Triangle :
Area =$\frac{1}{2}\times b\times h$
Perimeter = Sum of all sides

Isosceles right angle triangle :
Area = $\frac{1}{2}\times b\times h$
Perimeter = $2a+d$, where $d=a\sqrt{2}$

Equilateral Triangle :
Area = $\frac{\sqrt{3}}{4}{a}^2$
Perimeter = $3a$

Trapezium :
Area =$\frac{1}{2}h\times$(sum of parallel sides)$
Perimeter = Sum of all sides

Rhombus :
Area = $\frac{1}{2}\times d_1\times d_2$ where $d_1,d_2$ are diagonals
Perimeter = $4l$

Quadrilateral
Area = $\frac{1}{2}\times b\times h$

Kite :
Area = $\frac{1}{2}\times d_1\times d_2$, where $d_1,d_2$ are diagonals
Perimeter = $2\times$ Sum on non-adjacent sides

Circle :
Area = $\pi r^2$
Circumference = $2\pi r$
Area of sector of a circle = $\frac{\theta \pi r^2}{{360}^{\circ }}$

Frustum :
Curved surface area = $\pi h(r_1+r_2)$
Surface area = $\pi (r_1^2+h(r_1+r_2)+r_2^2)$

Cube :
Volume: V = $a^3$
Lateral surface area = $4a^2$
Surface Area: S = $6a^2$
Diagonal (d) = $\sqrt{3}a$

Cuboid :
Volume of cuboid: $lbh$
Total surface area = $2(lb+bh+hl)$
Length of diagonal = $\sqrt{(l^2+b^2+h^2)}$

Right Circular Cylinder :
Volume of Cylinder = $\pi r^{2}h$
Lateral Surface Area (LSA or CSA) = $2\pi rh$
Total Surface Area = TSA = $2\pi r(r+h)$
Volume of hollow cylinder = $\pi rh(R^2–r^2)$

Right Circular cone :
Volume = $\frac{1}{3}\pi r^{2}h$
Curved surface area: CSA= $\pi rl$
Total surface area = TSA = $\pi r(r+l)$

Sphere
Volume: V = $\frac{4}{3}\pi r^3$
Surface Area: S = $4\pi r^2$

Hemisphere :
Volume = $\frac{2}{3}\pi r^3$
Curved surface area(CSA) = $2\pi r^2$
Total surface area = TSA = $3\pi r^2$

Prism :
Volume = Base area $\times$ h
Lateral Surface area = perimeter of the base $\times$ h

Pyramid:
Volume of a right pyramid = $\frac{1}{3}$ $\times$ area of the base $\times$ height.
Area of the lateral faces of a right pyramid = $\frac{1}{2}$ $\times$ perimeter of the base $\times$ slant height.
Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Tetrahedron :
Area of its slant sides = $3a^2\frac{sqrt3}{4}$
Area of its whole surface = $\sqrt{3}{a}^2$
Volume of the tetrahedron = $\frac{\surd 2}{12}{a}^3$

Regular Hexagon :
Area = $3\times \frac{\sqrt{3}{a}^2}{2}$
Perimeter = $6a$

Some other Formula :
Area of Pathway running across the middle of a rectangle = $w(l+b-w)$
Perimeter of Pathway around a rectangle field = $2(l+b+4w)$
Area of Pathway around a rectangle field = $2w(l+b+2w)$
Perimeter of Pathway inside a rectangle field = $2(l+b-4w)$
Area of Pathway inside a rectangle field = $2w(l+b-2w)$
Area of four walls = $2h(l+b)$