The diagonal of a square is 8 ft. Find the circumference and tha area of a circle inscribed in the square.
First, determine the length of the sides of the square. To do so, consider the given diagonal and apply Pythagorean formula.
Now that the length of the sides is known, we need to take note that the diameter of a circle inscribed in a square is equal to its side.
Hence, the diameter of the circle is 4sqrt2 ft. And its radius is:
`r = d/2=(4sqrt2)/2`
Now that the radius is known, proceed to solve for the circumference and area of the circle.
The formula for circumference and area of circle are:
`C=2pir` and `A= pir^2`
Plug-in the value of r to each formula.
`A= pi(2sqrt2)^2= pi(4*2)=8pi`
Hence, the circumference of the circle is `4sqrt2pi` ft and its area is `8 pi` square ft.
L (square side ) is D `sqrt(2)` /`2` D diagonal
the half side L is the radius of the circle we'r seaching for:
`R` `=` `D` `sqrt(2)` /`4`
so the cirumference C is:
`C` `=` `2``pi` `R` =`D` `pi` `sqrt(2)` /`2` `=` `17,710` `ft`
the Area A is:
`A` `=` `pi` `R` `^2` =`pi` `D` `^2` / `8` =`25,12` `ft` `^2`