Mensuration

Solution:

1. Identify the given options for combining shapes: A, B, C; B, C, E; B, D, E; A, D, E.
2. Evaluate the lengths and angles of each option to check if they can form a rectangle.
3. Option B, D, E must be assessed: they allow for opposite sides to be parallel and equal, fitting together to form four right angles. Specifically:
   • Shape B may serve as one set of opposite sides.
   • Shape D can provide the connecting edges that lead to right angles at each corner.
   • Shape E can complement by filling the remaining sides to complete the rectangle.

Thus, the combination of shapes B, D, and E forms a rectangular figure. This is because the shape arrangement allows for opposite sides being parallel and equal, with connecting angles ensuring right angles are present. Other options do not satisfy all conditions for constructing a rectangular figure. Therefore, the correct answer is B, D, E.

1. The diameter of the circle is twice the radius, so for our circle, the diameter is 2 * 2 = 4 cm.
2. Consider a rectangle with length and width . The diagonal of the rectangle (which is also the diameter of the circle) can be expressed as:
   .
   Given, ,
   we have:
   
3. Square both sides:
   
4. The area of the rectangle is given by:
   .
   To maximize , consider using (i.e., it is a square), because for a fixed diagonal, a square has the maximum area.
5. With :
   
   
   
   
6. The maximum area becomes:
   cm².