A regular heptagon (7 sides) has perimeter 126 and area A. Express the apothem a of the heptagon algebraically in terms of the area A.

Kim is building a large gazebo for her backyard. It is in the shape of a regular hexagon. Each side of the gazebo is 12 feet long. The apothem is 10.4 feet. She needs to purchase stones for the floor. It costs $9.50 per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor. Round to the nearest ten dollars.

An irregular plane figure drawn on graph paper is framed inside of a 15 by 40 rectangle. To find its area, 10,000 random points are generated, and 5,710 of them land inside the irregular region. What is the area of the irregular region, to the nearest integer?

A regular heptagon (7 sides) has perimeter 126 and area A. Express the apothem a of the heptagon algebraically in terms of the area A.

The length of a room is $19 \frac{1}{2}$ feet. When using $\frac{1}{4}$ inch = 1 foot scale, what would be the length of the wall on a floor plan?

A rectangular room has length L and width W, where L and W are measured in feet. If carpeting costs x dollars per square yard, express the cost of carpeting this room algebraically.

The main meeting room of the Glen Oaks Community Center measures 46 feet by 34 feet and has a 12-foot ceiling. It is well insulated and faces the east side of his house. The manager wants to purchase an air conditioner. How large an air conditioner should he purchase? Round up to the next thousand BTUs.

A rectangular room has length L and width W. Its volume is 2,455 cubic feet. Express the height of the ceiling algebraically in terms of x.

Kim is building a large gazebo for her backyard. It is in the shape of a regular hexagon. Each side of the gazebo is 12 feet long. The apothem is 10.4 feet. She needs to purchase stones for the floor. It costs $9.50 per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor. Round to the nearest ten dollars.

Let G be an r-regular graph with n vertices and m edges. Find (and prove) a simple algebraic relation between r, n, and m.

A regular polyhedron has axis symmetry of order 3, but does not have plane symmetry. What is the figure? Explain.

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 72

What is the relationship between the side length and the apothem in each figure? a. a square b. a regular hexagon c. an equilateral triangle

A card is drawn at random from a regular deck of 52 cards. Find the probability of each event. A spade is drawn.