A square pyramid has base PQRS and vertex O. Each edge has length equal to 20. Calculate the shortest distance along the outer surface of the pyramid from P to T, the midpoint of OR.
A certain right pyramid with a square base has the same numerical surface area as its volume. If it is also the only right pyramid with a square base to have that certain surface area and volume, what is its height?
A square has side length equal to 1 meter. A circle is constructed through one corner of the square and tangent to the opposite two sides of the square. What is the area shaded in blue below, which is the area contained by the square and circle excluding the region where the two shapes overlap?
A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC. What is the area of the square?
A teacher has a rope with length equal to L cm. Using the entire rope, he forms the edges of a non-square rectangle with area equal to A cm2. What is the length of the smaller side of this rectangle, in cm ? (In terms of L and A)
A circle has a radius of 12 units and its center is at one vertex of a square. The square has a side of 12 units. Find the area of the shaded region?
