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Diameters AE and BD of length 6cm form the sides of congruent equilateral triangles ABC and CDE which are circumscribed by circles. Find the combined area of the shaded lunes, which include the area inside the smaller circles but outside the larger circle.
A cone has a radius of 6 cm and a height of 20 cm is half-full of water (by volume). What is the depth of the water in the cone to the nearest tenth of a centimeter?
An icosahedron has 20 faces, all of which are equilateral triangles. How many vertices are there on a regular icosahedron?
The areas of the faces of a right rectangular prism are 6, 9, and 12 cm square. To the nearest tenth of a centimeter, what is the length of the diagonal of the prism?
What is the difference in area between the inscribed circle and the circumscribed circle in a 12-gon of edge length 2 cm?
On square ABCD, E is the midpoint of side AB. Diagonal AC intersects segment ED at X. Find the length of segment EX if AB = 6cm.
The diagonals of right trapezoid are perpendicular. What is the area of the trapezoid if the parallel bases measure 8 cm and 18 cm?