Question

Willow works for the local council and one of their projects is to renovate the town hall. They intend to refurbish the dance floor that is shaped like this.

Scale = 1cm: 2m

Calculate the actual area of the dance floor. Show all working.

Answer 1

96m²

Explanation:

Think of the sclae as 2m per 1cm so you can write that as a fraction and use it as a conversion factor:

`(2m)/(1cm)`

As a whole square, the actual dimensions of the dance floor would be:

`5cm *(2m)/(1cm)=10m`

So each side is actually 10m.

We can use that to solve for the whole square:

A = s²

Where s = side of a square

A = (10m)² = 100m²

Now all you need to do is solve for the are of the missing corner. Consider that missing corner is a right triangle. It's legs are 1cm long and 2 cm long.

If we convert get the actual length it would be: 2m and 4m.

The area of the right triange would be:

`A = (ab)/(2)`

Where:

a and b are the two legs of the right triangle (NOT THE HYPOTENUSE, or longest side)

So:

a = 2m

b = 4m

Now plug that into our formula:

`A = (ab)/(2)\\\\A = (2m*4m)/(2)\\\\A = (8m^2)/(2)\\\\A = 4m^2`

Then now we take the area of the missing side and subtract it from the whole square:

Area of the whole square - Area of the missing corner (right triangle)

100 m² - 4m² = 96m²