**Formulas for 2D Shapes**

Assume that $l, b$ represent length and breadth of a 2D shape.

**(1) Rectangle**

Perimeter = $2(l + b)$

Area = $l \times b$

**(2) Square**

Perimeter = $4 \times side$

Area = $(side)^2$

**(3) Parallelogram**

Perimeter = $2(l + b)$

Area = $l \times b$

**(4) Triangle**

**Scalene Triangle**

Let $a, b, c$ be the length of three sides of a triangle.

Perimeter $(2s)$ = $a + b + c$

Semi perimeter $(s)$ = $\frac{a+b+c}{2}$

Area = $\sqrt{s(s-a)(s-b)(s-c)}$ This is called Heron’s formula.

Area = $\frac{1}{2}$ $base \times height$

**Isosceles Triangle**

Let a being the measure of two equal sides and b be the base.

Perimeter = $2a + b$

Area = $\frac{b \sqrt{4a^2-b^2}}{4}$

**Equilateral Triangle**

Perimeter = $3 \times side$

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

**(5) Trapezium**

Perimeter = Sum of $4$ sides

Area = $\frac{1}{2}$ $\times$ sum of parallel sides $\times$ distance between parallel sides

**(6) Rhombus**

Perimeter = $4 \times side$

Area = $\frac{1}{2}$ product of diagonals

**(7) Circle**

Let $r$ be the radius of circle.

Diameter = $2r$

Circumference = $2 \pi r$

Area = $\pi r^2$

**(8) Semicircle**

Circumference = $\pi r$

Area = $\frac{1}{2}$ $\pi r^2$

**Formulas for 3D Shapes**

(Assume that $l, b, h$ stand for length, breadth, height respectively in a 3D shape.)

**(1) Cuboid**

Lateral surface area = $2(l + b) \times h$

Total surface area of cuboid = $2(lb + bh + hl)$

Volume = $l, b, h$

**(2) Cube**

Lateral surface area = $4a^2$

Total surface area = $6a^2$

Volume of cube = $side^3$

**(3) Cylinder**

Curved surface area = $2 \pi rh$

Total surface area = $2 \pi r(h + r)$

Volume = $\pi r^2 h$

Where, $r$ being the radius of base and $h$ is the height.

**(4) Cone**

Slant height $(l)$ = $\sqrt{h^2 + r^2}$

Curved surface area = $\pi r\ l$

Total surface area = $\pi r\ (l + r)$

Volume = $\frac{1}{3}$ $\pi r^2 h$

**(5) Sphere**

Curved surface area = Total surface area = $4 \pi r^2$

Volume = $\frac{4}{3}$ $\pi r^3$

**(6) Hemisphere**

Curved surface area = $2 \pi r^2$

Total surface area = $3 \pi r^2$

Volume = $\frac{2}{3}$ $\pi r^3$

**(7) Prism**

Lateral surface area = perimeter of base $\times$ height

Total surface area = Lateral surface area $+\ (2 \times$ area of base)

Volume = Area of base $\times$ height

**(8) Pyramid**

Lateral surface area = $\frac{1}{2}$ $\times$ Perimeter of base $\times$ slant height

Where, slant height = Height of the lateral triangular surface

Total surface area = Lateral surface area + area of base

Volume = $\frac{1}{3}$ $\times$ area of base $\times$ height