For optimization problems, the following results will be very useful.

1) For a square of side 'x', we have,

Area = $x^{2}$ and Perimeter = 4x.

2) For rectangle of sides x and y, we have,

Area = xy and Perimeter = 2(x + y)

3) For trapezoid, we have,

Area = 1/2( a + b)*h where a and b are two opposite parallel sides and h is the height.

4) For circle of radius r, we have,

Area = $\pi r^{2}$ , Circumference = r$\pi$r

5) For sphere of radius r, we have ,

Surface area = 4$\pi r^{2}$ , Volume = 4/3 $\pi r^{3}$

6) For a right circular cylinder of base radius r and height h, we have

Surface area = 2$\pi$ r(r + h), Curved surface area = 2$\pi$ rh, Volume = $\pi r^{2}$ h

7) For right circular cone of height h, slant height 'l' and radius of the base r, we have

Surface area = $\pi$ r (r + l) , Curved surface area = $\pi$ r l , Volume = 1/3 $\pi r^{2}$ h

8) For a rectangular prism of length x , y and z, we have

Surface area = 2(xy + yz + xz) and Volume = xyz

9) For a cube of edge length x, we have

Surface area = 6$x^{2}$ , Volume = $x^{3}$

10) Area of equilateral triangle = $\frac{\sqrt{3}(side)^{2}}{4}$

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