An octagon with equal side lengths is made by cutting the corners from a rectangle that has sides of 4 and 6, as shown below. What is the side length of the octagon?
~2.14
As per below picture, we have: x=c 2a+x=4 ---> (1) => a=2-x/2 2b+x=6 ---> (2) => b=3-x/2 x^2=a^2+b^2 ---> (3) Considering (1) and (2) in (3) we get x^2+10x-26=0 ---> x~ 2.14
A regular hexagon with side length 2 has semicircles constructed in its interior of each side. What is the shaded area inside the hexagon not covered by the semicircles?
The diagonals of a convex quadrilateral are perpendicular. If three sides are equal to 3, 2, and 1, as shown, what is the length of the fourth side?
In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram. What is the radius of the inscribed circle?
The square ABCD has a side length of 1, and AEF is an equilateral triangle. What is the area of AEF?
