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.

96m²

Step-by-step explanation:

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

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

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:

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:

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