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: 2mCalculate the actual area of the dance floor. Show all working.

Answer:96m²Step-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:[tex]\dfrac{2m}{1cm}[/tex]As a whole square, the actual dimensions of the dance floor would be:[tex]5cm \times\dfrac{2m}{1cm}=10m[/tex]So each side is actually 10m.We can use that to solve for the whole square:A = s²Where s = side of a squareA = (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:[tex]A = \dfrac{ab}{2}[/tex]Where:a and b are the two legs of the right triangle (NOT THE HYPOTENUSE, or longest side)So:a = 2mb = 4mNow plug that into our formula:[tex]A = \dfrac{ab}{2}\\\\A = \dfrac{2m\times4m}{2}\\\\A = \dfrac{8m^2}{2}\\\\A = 4m^2[/tex]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