Perimeter and area of composite shapes involving circles

Task goals

• Calculate the perimeter of a composite shape made from a rectangle or square with a semicircle attached to one side, using pi approximately equal to 3.14.
• Calculate the area of a composite shape made from a rectangle or square with a semicircle attached to one side, using pi approximately equal to 3.14.
• Calculate the remaining perimeter or area of a square or rectangle after a quarter circle has been cut from one corner, using pi approximately equal to 3.14.
• Calculate the perimeter and area of a stadium or running-lane shape made from two straight sides and two semicircular ends, using pi approximately equal to 3.14.
• Calculate a composite perimeter or area in exact form, leaving the answer in terms of pi, for the same rectangle-plus-circle and square-minus-quarter-circle shapes.
• Find the area inside a square but outside an inscribed circle formed by four quarter circles drawn at its corners, or the total curved length of those quarter circles, in terms of pi.
• Given the total perimeter or area of a composite circle-rectangle shape expressed in terms of pi, work backwards to find an unknown side length or radius.
• Solve a composite-shape perimeter or area problem set in a real-world context, such as finding the cost of fencing around a composite shape, with the answer in terms of pi.