Challenge Problems

Find the missing area. 

Five congruent rectangles are arranged to form a rectangle as shown. The perimeter of the large rectangle is 308mm, Find the perimeter of a small rectangle.

Find the shaded area. (This one looks impossible. But it is good practice for the strategy of carefully determining what you know, and thinking about what you need. Once you've thought about both of those questions, this may just fall apart in your hands.) The line is tangent to the inner circle, and the two circles are concentric. Find the orange area.

 The graph below shows how much water is in the tank at time t. Water comes in at A, and drains out at B.

1. 1. • How much water enters through the faucet at A in one minute?

      • For how many minutes is the drain at B open?

      • How much water drains out through the drain at B in one minute?

A laser shines into our reflective box (shown below) at the origin. Find the value of a so that the light bounces at the point (1/2, 0).