Answer:
258 square centimeters
Step-by-step explanation:
Consider the image attached below.
We can see that the length of each side of L shape is 40 cm and in 2 plates fit in between.
We need to find the are which is not covered by the plates. Let us calculate the area of L shape first.
We can see that it is a square with one fourth of its area missing. So the area of square with side length 40 cm is,
[tex]A_1= 40 \times 40 = 1600 cm^2[/tex], where '[tex]A_1[/tex]' is the area of square.
Now, one fourth of the area is not there in the L shape, so one-fourth of [tex]1600cm^2[/tex] is,
[tex]\frac{1600}{4}= 400 cm^2[/tex]
Therefore, the area of L shape drawer is,
[tex]1600-400=1200 cm^2[/tex]
Now, we can see that the diameter of each circular plate is, 20 cm. So the radius of circular plate is 10 cm. Let [tex]A_2[/tex] be the area of each circular plate, so,
[tex]A_2= \pi (10)^2=100\pi cm^2[/tex]
There are three plates so the total area is,
[tex]A_3= 3\times 100 \pi = 300 \pi cm^2[/tex]
[tex]A_3= 300\times 3.14 = 942 cm^2[/tex]
Hence, the area not covered by the plates is,
= [tex]1200-942= 258 cm^2[/tex]
So, the area not covered by three flat plates is 258 square centimeters.
