Algebra in measurement

There are lots of different measurement formulae we use for lots of different things in maths. We can write a formula for a shapes perimeter, area or volume, just to name a few. We've already learnt how to write and substitute values into common formulae. When we did this, we'd write a formula algebraically, then substitute in a number value, the find another unknown. For example, if we were asked to find the area of a square with $5$5cm sides, we'd write the formula for the area of a square ($A=s^2$A=s2), then substitute in the side length ($A=5^2$A=52) to work out that the area of the square is $25$25 $cm^2$cm2.

Now we are going to look at examples of shapes where the side lengths contain algebraic terms, not just numbers. But don't freak out! As long as you know your measurement formulae, we can substitute these terms in just the same way as we would if they were numbers, then simplify the expression by grouping any like terms.

Examples

Question 1

Write an expression for the perimeter of the rectangle below.

Question 2

Write an expression for the area of the triangle below.

 

Question 3

Consider the rectangular prism below.

a) Write an expression for its volume.

b) Write an expression for its surface area.