The solid represented by the Mat Plan is built and glued together. The solid is dipped in red paint and then left to dry. Once dried, the cubes are broken apart and each cube is dropped into a bag. If you are going to reach into the bag and pull out a cube at random, what is the probability that the cube has at least one red face?

Margaret has just received a letter from her pen pal Clarissa in Boston. Clarissa's letter describes their backyard by saying:

"It is a triangle with one side 60 feet long, one side 44 feet long, and the third side 36 feet long."

Margaret measures her own backyard which is also a triangle and finds its sides are also 60 feet, 44 feet, and 36 feet. Are the two yards congruent in shape? Explain why or why not.

As Winter Recess approaches, you and some friends plan to construct a kid's toboggan slope on a patch of open land owned by your uncle. Kristin built a scale model. The model required 11 feet of rope to represent the fencing and 1.65 cubic feet of clay to represent the snow hill. If the scale of the model is 1:32, how much fencing and snow will be needed for the toboggan run?

Calculate the total surface area and the volume of the given prism. The bases are parallelograms. All vertical edges are perpendicular to the bases. Show all subproblems.

Is it true that if an n-gon is nonconvex, then the sum of the interior angles is still found by using (n - 2)180$^{\circ}$? Either prove it for the given figure or else give a counterexample.

Describe the effect that increasing the number of sides of a regular n-gon has on the area of the n-gon when the length of the side remains the same.

Does it make sense to connect the points? Explain.

Based on your graph, make predictions for the areas of a regular 8-gon, 9-gon, and 11-gon with side lengths of 12. Mark these points (preferably with a different color) on your graph.

Plot the given areas and those for regular 5-, 7-, and 10-gons from the previous problems on the resource page provided.

Use your work from the previous three problems to describe a general method (that is, a sequence of subproblems) for calculating the area of any regular n-gon.

Jabari is trying to find the sum of the measures of the interior angles of a 100-gon. You notice that he is trying to draw a 100-gon! When you ask him why he is trying to draw it, he says, "I need to draw in all the triangles just like I did on the resource page." Explain to Jabari how to do this problem without drawing a 100-gon and without drawing in all the triangles.

Jabari is trying to find the sum of the measures of the interior angles of a 100-gon. You notice that he is trying to draw a 100-gon! When you ask him why he is trying to draw it, he says, "I need to draw in all the triangles just like I did on the resource page." If Jabari does draw in all the triangles, as you did on the resource page, how many triangles will he have?

Use the process developed in the previous two problems to find the area of a regular 10-gon with a side length of 12'' and center at A. Part of the figure is shown.

The figure is a regular 7-gon with center at P and segments OB and XY are perpendicular. If QR = 12'', find the area of the 7-gon. If you need help, some of the subproblems are listed below and details are modeled in the preceding problem.

What is the measure of angle QRS? measure of angle 1?

What is PB?

What is the area of triangle PQR?