Assignment 5 (Due Friday at the beginning of class)

Problem 1. In the figure below, the area of the big circle is A. What is the area of the unshaded area inside the big circle and outside the shaded circles? Explain your reasoning briefly.
Problem 2. In the figure below, the length of AB = 2, the length of BC = 3, the length of BD = 4/3. Show that the triangles ABC and ABD are similar. What are the corresponding vertices? What is the scale factor from ABC to ABD? If length AC = 5/2, what is length AD?

Ending up. Complete or Incomplete

The expectation for Complete on Assignments is (approximately) 3.0 on the parts of the homework.

There are a number of Assignments that need some makeup to get to the level of Complete. You will get the word on Assignment 1 and 2 today. If you are pretty sure you need to rework some of the latter, you can go ahead now or wait for the word tomorrow.

Also, if you are shooting for a 4.0, you should consider an Extension or a Challenge problem if you have not already done one or more.

More Challenge Problems

General Cake: For the same kind of cake as before, iced on top and sides, try to divide these cakes with equal volumes of cake and equal amounts of top frosting and equal amounts of side frosting. (All cakes are prisms on some base as described.)

• Divide a regular pentagonal cake into 6 parts.
• Divide a rectangular cake into 5 parts.
• Divide a cake in the shape of random, general triangle, into 4 equal parts.

Extension

Make a Nice Model: Make a good cut-away model of the tetrahedron problem from Assignment 4, showing the altitude and triangles inside.

Propose Your Own extension or challenge.