1. Find the area of the figure. Round to the nearest tenth if necessary.
Lesson 3 Menu

2. Find areas of regular polygons.
Find areas of circles.
apothem
Lesson 3 MI/Vocab

3. Lesson 3 KC1

4. Area of a Regular Polygon
Find the area of a regular pentagon with a perimeter of 90 meters.
Lesson 3 Ex1

5. Area of a Regular Polygon
Apothem: The central angles of a regular pentagon are all congruent. Therefore, the measure of
each angle is or is an apothem
of pentagon ABCDE. It bisects and is a perpendicular bisector of So, or 36. Since the perimeter is 90 meters, each side is 18 meters and meters.
Lesson 3 Ex1

6. Area of a Regular Polygon
Write a trigonometric ratio to find the length of
Multiply each side by GF.
Divide each side by tan .
Use a calculator.
Lesson 3 Ex1

7. Area of a Regular Polygon
≈ 557
Simplify.
Answer: The area of the pentagon is about 557 square meters.
Lesson 3 Ex1

8. Find the area of a regular pentagon with a perimeter of 120 inches
Find the area of a regular pentagon with a perimeter of 120 inches. To the nearest square inch.
A. 890 in2
B in2
C. 991 in2
D in2 A B C D
Lesson 3 CYP1

9. Lesson 3 KC2

10. An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square yards.
The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So the diameter of the cover is or 88 inches. Divide by 2 to find that the radius is 44 inches.
Lesson 3 Ex2

11. Area of a circle Substitution Use a calculator.
The area of the cover is square inches. To convert to square yards, divide by 1296.
Answer: The area of the cover is 4.7 square yards to the nearest tenth.
Lesson 3 Ex2

12. A swimming pool company manufactures circular covers for above ground pools. If the cover is 10 inches longer than the pool on each side, find the area of the cover in square yards. A B C D
A yd2
B yd2
C yd2
D yd2
Lesson 3 CYP2

13. Area of an Inscribed Polygon
Find the area of the shaded region. Assume that the triangle is equilateral. Round to the nearest tenth.
The area of the shaded region is the difference between the area of the circle and the area of the triangle. First, find the area of the circle.
Area of a circle
Substitution
Use a calculator.
Lesson 3 Ex3

14. Area of an Inscribed Polygon
To find the area of the triangle, use properties of 30-60-90 triangles. First, find the length of the base. The hypotenuse of so RS is 3.5 and SZ Since Δ
Lesson 3 Ex3

15. Area of an Inscribed Polygon
Next, find the height of the triangle, XS. Since m
Area of a triangle
Use a calculator.
Answer: The area of the shaded region is – 63.7 or 90.3 square centimeters to the nearest tenth.
Lesson 3 Ex3