## Math 3118 Practice Exam 2 Fall 2001

### Practice Exam 2-1

1. Find the area of the region outside the circle but inside the parallelogram, see picture1.

2. Find any primitive Pythagorean triple (a,b,c) with b=48.

3. Give a formula for the area of a parallelogram, and explain why it is true.

4. True or False: Suppose we have a right triangle whose legs have lengths x and y. If we make a new right triangle whose legs have lengths 2x and 2y, then the new hypotenuse will be twice as long as the original hypotenuse.

5. Find a formula for the area of a parallelogram, all of whose sides have length s, and whose angles are 45 degrees, 135 degrees, 45 degrees, and 135 degrees.

6. Find the area of a square inscribed in a circle of radius 1, and give an inequality for \pi based on your calculation.

### Practice Exam 2-2

1. Find all primitive Pythagorean triples which have b=24.

2. True or False: If (a,b,c) and (a',b',c') are both Pythagorean triples, then (a+a', b+b', c+c') is another Pythagorean triple.

3. Suppose that two sides of triangle b and c are fixed.

(a) Show that a must be less than b+c.
(b) True or False: As a increases from 0 to b+c, the area of the triangle increases.

4. Explain why \pi must be larger than 3.

### Practice Exam 2-3

1. Find the area of the region picture2, which includes a trapezoid and 2 triangles. The angles of the trapezoid are 45, 135, 135, and 45.

2. True or False: There is no primitive Pythagorean triple (a,b,c) with c=108.

3. Show that (39,80,89) is a primitive Pythagorean triple.

4. Which has a larger area? A circle of radius 2, or a square of side \sqrt(12)?

5. Find the area of a regular hexagon of whose side length is s.