Question

Janna has three flat plates easy the same size. She stores them in an L shaped drawer as shown so that they fit snuggly inside with no space between the edges of the drawer and the plates. Approximately how many square centimeters of the bottom of the drawer are not covered by plates? Pls help me!! Also, explain how you got the answer. They’re 40 cm.

Answer 1

258 square centimeters

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,

`A_1= 40 * 40 = 1600 cm^2`, where '
`A_1`' is the area of square.

Now, one fourth of the area is not there in the L shape, so one-fourth of
`1600cm^2` is,

`(1600)/(4)= 400 cm^2`

Therefore, the area of L shape drawer is,

`1600-400=1200 cm^2`

Now, we can see that the diameter of each circular plate is, 20 cm. So the radius of circular plate is 10 cm. Let
`A_2` be the area of each circular plate, so,

`A_2= \pi (10)^2=100\pi cm^2`

There are three plates so the total area is,

`A_3= 3* 100 \pi = 300 \pi cm^2`

`A_3= 300* 3.14 = 942 cm^2`

Hence, the area not covered by the plates is,

=
`1200-942= 258 cm^2`

So, the area not covered by three flat plates is 258 square centimeters.