# Exercises: Solve Geometry Applications: Circles and Irregular Figures (6.3)

## Exercises: Use the Properties of Circles

Instructions: For questions 1-14, solve using the properties of circles.

1. The lid of a paint bucket is a circle with radius $7$ inches. Find the

a. circumference and
b. area of the lid.

Solution

a. $43.96$ in.
b. $153.86$ sq. in.

2. An extra-large pizza is a circle with radius $8$ inches. Find the

a. circumference and
b. area of the pizza.

3. A farm sprinkler spreads water in a circle with radius of $8.5$ feet. Find the

a. circumference and
b. area of the watered circle.

Solution

a. $53.38$ ft
b. $226.865$ sq. ft

4. A circular rug has radius of $3.5$ feet. Find the

a. circumference and
b. area of the rug.

5. A reflecting pool is in the shape of a circle with diameter of $20$ feet. What is the circumference of the pool?
Solution

$62.8$ ft

6. A turntable is a circle with diameter of $10$ inches. What is the circumference of the turntable?

7. A circular saw has a diameter of $12$ inches. What is the circumference of the saw?
Solution

$37.68$ in.

8. A round coin has a diameter of $3$ centimeters. What is the circumference of the coin?

9. A barbecue grill is a circle with a diameter of $2.2$ feet. What is the circumference of the grill?
Solution

$6.908$ ft

10. The top of a pie tin is a circle with a diameter of $9.5$ inches. What is the circumference of the top?

11. A circle has a circumference of $163.28$ inches. Find the diameter.
Solution

$52$ in.

12. A circle has a circumference of $59.66$ feet. Find the diameter.

13. A circle has a circumference of $17.27$ meters. Find the diameter.
Solution

$5.5$ m

14. A circle has a circumference of $80.07$ centimeters. Find the diameter.

## Exercises: Use the Properties of Circles

Instructions: For questions 15-18, find the radius of the circle with given circumference.
15. A circle has a circumference of $150.72$ feet.
Solution

$24$ ft

16. A circle has a circumference of $251.2$ centimeters.

17. A circle has a circumference of $40.82$ miles.
Solution

$6.5$ mi

18. A circle has a circumference of $78.5$ inches.

## Exercises: Find the Area of Irregular Figures

Instructions: For questions 19-38, find the area of the irregular figure. Round your answers to the nearest hundredth.

19.

Solution

$16$ sq. units

20.

21.

Solution

$30$ sq. units

22.

23.

Solution

$57.5$ sq. units

24.

25.

Solution

$12$ sq. units

26.

27.

Solution

$67.5$ sq. units

28.

29.

Solution

$89$ sq. units

30.

31.

Solution

$44.81$ sq. units

32.

33.

Solution

$41.12$ sq. units

34.

35.

Solution

$35.13$ sq. units

36.

37.

Solution

$95.625$ sq. units

38.

## Exercises: Find the Area of Irregular Figures

Instructions: For questions 39-42, solve.
39. A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides $250$ feet long, and the triangles are isosceles right triangles. Find the area of the park.

Solution

$187\text{,}500$ sq. ft

40. A gift box will be made from a rectangular piece of cardboard measuring $12$ inches by $20$ inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are $3$ inches. Find the area of the cardboard after the corners are cut out.

41. Perry needs to put in a new lawn. His lot is a rectangle with a length of $120$ feet and a width of $100$ feet. The house is rectangular and measures $50$ feet by $40$ feet. His driveway is rectangular and measures $20$ feet by $30$ feet, as shown. Find the area of Perry’s lawn.

Solution

$9400$ sq. ft

42. Denise is planning to put a deck in her back yard. The deck will be a $\text{20-ft}$ by $\text{12-ft}$ rectangle with a semicircle of diameter $6$ feet, as shown below. Find the area of the deck.

## Exercises: Everyday Math

Instructions: For questions 43-44, answer the given everyday math word problems.

43. Area of a Tabletop Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a $\text{1-ft}$ by $\text{3-ft}$ rectangle with a semicircle at each end, as shown.

a. Find the area of the table with one leaf up.
b. Find the area of the table with both leaves up.

Solution

a. $6.5325$ sq. ft
b. $10.065$ sq. ft

44. Painting Leora wants to paint the nursery in her house. The nursery is an $\text{8-ft}$ by $\text{10-ft}$ rectangle, and the ceiling is $8$ feet tall. There is a $\text{3-ft}$ by $\text{6.5-ft}$ door on one wall, a $\text{3-ft}$ by $\text{6.5-ft}$ closet door on another wall, and one $\text{4-ft}$ by $\text{3.5-ft}$ window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?

## Exercises: Writing Exercises

Instructions: For questions 45-46, answer the given writing exercises.

45. Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.

Solution

46. A circle has a diameter of $14$ feet. Find the area of the circle
a. using $3.14$ for$\pi$
b. using $\frac{22}{7}$ for $\text{π}.$