Answer:
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:
[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 = 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:
[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 = 2m
b = 4m
Now 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
