Regular Polygons and Sectors of Circles

A regular octagon has a perimeter of 96 feet. The apothem of the polygon is 9 feet. What is the length of a side of the octagon?

• 10 ft

• 12 ft

• 14 ft

• 15 ft

A regular octagon has a perimeter of 96 feet. The apothem of the polygon is 9 feet. What is the area of the regular octagon?

• 54 ft²

• 108 ft²

• 432 ft²

• 864 ft²

The diagram is a composite figure comprised of a combination of two shapes. Which two areas can be added to find the area of the composite figure?

• 30 cm²

• 60 cm²

• 18π cm²

• 36π cm²

• 120 cm²

Half of the main entrance of a mansion is shown in the diagram? What is the area of the shaded region? Round your answer to the nearest hundredth.

• 369.10 ft²

• 381.66 ft²

• 256.00 ft²

• 356.57 ft²

Jocelyn and Bryan designed a spinner with ten equal sides and five identical sectors around the spinner as shown in the diagram. Without the sectors, the perimeter of the spinner is 60 cm, and its apothem is about 9.2 cm.

What is the area of the five identical sectors? Round your answer to the nearest hundredth.

• 11.31 cm²

• 226.19 cm²

• 56.55 cm²

• 113.10 cm²

Jocelyn and Bryan designed a spinner with ten equal sides and five identical sectors around the spinner as shown in the diagram. Without the sectors, the perimeter of the spinner is 60 cm, and its apothem is about 9.2 cm.

What is the area of the spinner as a composite figure? Round your answer to the nearest hundredth.

• 332.55 cm²

• 287.31 cm²

• 413.10 cm²

• 502.19 cm²

• 97.3

• 1401.12

• 700.56

• 600.48

Find the area of regular polygon.

$Formula\ A=\ \frac{1}{2}Pa$

• 891

• 792

• 108

• 1782