Suppose you are doing a puzzle. After 10 minutes, you have 275 pieces placed, and after 22 minutes, you have 395 pieces placed.
How many pieces will you have placed after an hour? Write your equation and answer in the text box, and graph the line on the coordinate plane.
1 answer:
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Answer:
The area of the shaded portion of the figure is
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shaded area is equal to the area of the square less the area not shaded.
There are 4 "not shaded" regions.
step 1
Find the area of square ABCD
The area of square is equal to
where
b is the length side of the square
we have
substitute
step 2
We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):
The area of circle is equal to
The diameter of the circle is equal to the length side of the square
so
---> radius is half the diameter
substitute
Therefore, the area of 2 "not-shaded" regions is:
and the area of 4 "not-shaded" regions is:
step 3
Find the area of the shaded region
Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:
so
---> exact value
assume
substitute
