### Overview

This builds on the Basic Algebra section. It covers; how to write your own algebraic formulae, how to evaluate expressions and formula by substituting values for variables and how to change the subject of a formula.

### Formulae Questions

**1.** Each side of a hexagon measure 4x +3. Write a formula for the perimeter of the hexagon.

**2.** Calculate these expressions when x = 2, y = 3 and z = –4.

**3. **The area of a triangle can be calculated from the formula:-

Area = √(s(s — x)(s — y)(s — z))

where s = (x + y + z)/2.

Find the area of a triangle which has sides of 6m, 8m and 10m.

**4. **Rearrange this formula to make x the subject:

y= (x³/6) + 4z

**5. **Rearrange this formula to make z the subject:

y = √(x/(z+5))

### Formulae Approach

**1.** I find that if I get stuck on creating a formula, it helps to jot down any relevant facts that I know. In this case it would be, “a hexagon has 6 sides” and “each side measures 4x +3″. This approach is more helpful the more complicated the question.

**2. & 3.** My approach is to re-write the formula substituting the numbers for the variables and then calculate the answer, taking care to do these in the right order (e.g. calculating the brackets first). With a complex expression I find it helps to re-write the expression as I calculate each part of it (see answers below to see exactly what I mean).

**4. & 5. **Again I find a step by step approach (and writing down each step) helps when rearranging formulas (see answers below).

### Formulae Answers

**1.** 6(4x + 3)

**2.** Calculate these expressions when x = 2, y = 3 and z = –4.

**3. **s = (6 + 8 +10)/2 = 12

Area = √(12(12 — 6)(12 — 8)(12 — 10))

= √(12 x 6 x 4 x 2)

= √(24 x 24)

= 24m²

**4. **y — 4z = x³/6

6y — 24z= x³

x = ³√(6y — 24z)

**5. **y = √(x/(z+5))

y² = x/z+5

y²(z + 5) = x

z + 5 = x/y²

z = x/y² - 5

owa, great post. Very thorough and well written. How long do you take to write a post like this one ?