Write the formulaformulaformula for the area of:

a) equilateral triangle,

b) any triangle,

c) trapezoid,

d) parallelogram.

Isolate the altitude of each polygon from its formulaformulaformula.

Isolate x from the formulaformulaformula.

a) $4bx+2a=c-cx$

b) $vx-5v=z(2x-v)$

From the following formulas isolate given variable. All variables are positive numbers. In the Internet look for relations in geometric figures than this formulas describe.

a) $P=ab+ah+bh$, isolate h

b) $P=\frac{a^2\sqrt{3}}{4}+2ah$, isolate h

c) $V=\frac{1}{3}{a}^{2}H$, isolate a

d) $V=\frac{a^2\sqrt{3}}{4}H$, isolate a

a) Isolate the length a of the longer base of a trapezoid whose area is 4p, if its altitude is 3x and the shorter base is z.

b) Isolate the length y of the shorter base of a trapezoid whose area is 2p is its altitude is 4h and the longer base is a.

An extra contest task:

Isolate a from the formulaformulaformula

Isolate x from the formula: $p(x-z)=2x-3$. Give necessary assumptions.

Look for formula for the area of the surface of a cuboid in the internet and isolate the length of one edge.

Present the solution in English.