a square is inscribed in a circle with radius r. find the area and the perimeter of the square in terms of r?

Answer 1

the diameter of the square will be the same as the diameter of the circle. so the surface can now be calculated since all unknowns can be derived from the diagonal length of the square.

Good luck with your carpeenter caareer

Answer 2

Make a quick sketch showing circle centre r inscribed within circle.
r cos 45° = r (1 /√ 2 )
Length of side of square = 2 r (1 /√ 2) = √2 r
Perimeter = 4√2 r
Area = √2 r x √2 r = 2 r ²

Answer 3

well assuming the square is in teh center or the circle...that means the side of the square is 2r

meaning the area is 2(2r) or 4r
and the perimeter is 4(2r) or 8r

Answer 4

Very simple! The circle radius is r so the squares sides are each 2r. Thus, square's area is 2r X 2r = 4 r-squared` and square's circumference is 2r+2r+2r+2r = 8 r
Take it easy...

Answer 5

Using the Pythagorean Theorem a^2+b^2=c^2:

AND since all sides are equal let a and b = s (side)

ALSO if: diameter = 2r, then c^2=(2r)^2

(2r)^2 = a^2+b^2
(2r)^2 = s^2+s^2
(2r)^2 = 2s^2
sqrt (2r)^2 = sqrt 2s^2
2r = 2s
r = s

therefore if P= 4s and A = l x w then

P= 4r units
A = r^2 sq. units