perimeter of quadrilaterals & triangles p = 4s

Math 6 NOTES (9.2a) Name ____________________________________

PERIMETER of Quadrilaterals & Triangles

___________________________________________ is the distance around a geometric figure.

One way to find perimeter is to _________________ the lengths of all the sides of a figure.

12 cm

6 cm Perimeter of Rectangle: _____________________________

_____________________________

6 in 8 in Perimeter of Triangle: _____________________________

4 in _____________________________ 7 in

Another way to find perimeter is to use a formula.

o The perimeter of a RECTANGLE: P = 2l + 2w

w = 10 mm Formula: _____________________________________

_____________________________________

_____________________________________

l = 16 mm Perimeter = _____________________________________

o The perimeter of a SQUARE: P = 4s

4 m Formula: _____________________________________

4m _____________________________________

Perimeter = _____________________________________

Examples (or key words) for when you use perimeter:

Fencing

Outline

Border

Framing

Around

Outside

You try!!

5m

3m 7cm

4m 14cm

AREA of Quadrilaterals

The ________________________ of a rectangle is the product of the length and the width.

The formula for the area of a rectangle is: A = l · w

10 cm Formula: _____________________________________

5 cm ____________________________________

_____________________________________

Area: _____________________________________

The formula for the area of a square is: A = s · s or A = s2

6 m Formula: _____________________________________

6 m _____________________________________

Area: _____________________________________

Key words (examples) for when you use area: -Area - Surface -Cover

- Curtain -Tile -Carpet

You Try! Find the area of each quadrilateral.

Area: __________ Area: ___________

4in

4in

8 cm

3 cm

AREA of Triangles

A triangle covers one half (

) of the area that a quadrilateral covers.

The formula for the area of a triangle is: A = 1

2b · h

The b is the base. The h is the height.

The ___________ of a ____________________ can be any of its sides.

The _________________ is the distance from a base to the opposite ________________.

Formula: ____________________________________ ____________________________________

Area: ____________________________________ You Try!

12m

7m

15 in

6 in

Math 6 Practice (9.2a)

Math 6 HW (9.2a)

© Glencoe/McGraw-Hill 343 Mathematics: Applications and Concepts, Course 2

Less

on

6–9

Find the circumference of a circle with a diameter of7.5 centimeters.

C 5 pd

C < 3.14 3 7.5 Use 3.14 for p.

C < 23.55 The circumference of the circle is about 23.55 centimeters.

If the radius of a circle is 14 inches, what is its circumference?

C 5 2pr

C < 2 3 }272} 3 14 Use }

272} for p.

C < 88 The circumference of the circle is about 88 inches.

Find the circumference of each circle. Use 3.14 or }272} for p. Round to

the nearest tenth if necessary.

1. 2. 3. 4.

5. diameter 5 15 km 6. radius 5 21 mi 7. radius 5 50 m

8. diameter 5 600 ft 9. radius 5 62 mm 10. diameter 5 7 km

11. radius 5 95 in. 12. diameter 5 6.3 m 13. diameter 5 5}14

} cm

7.5 in. 5 m

20 cm 6 ft

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention

Geometry: Circles and Circumference

A circle is the set of all points in a plane that are

the same distance from a given point, called the

center. The diameter d is the distance across the

circle through its center. The radius r is the

distance from the center to any point on the circle.

The circumference C is the distance around the

circle. The circumference C of a circle is equal to its

diameter d times p, or 2 times its radius r times p.

circumference

radius

center

diameter


Practice: Skills


Find the circumference of each circle. Use 3.14 or for p. Round tothe nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. radius 5 3 km 8. radius 5 46 cm

9. diameter 5 30 in. 10. diameter 5 25 m

11. radius 5 5 ft 12. diameter 5 9}12

} in.

13. radius 5 3}12

} ft 14. diameter 5 9.7 mm

15. radius 5 5.2 km 16. diameter 5 25 m

17. radius 5 22 ft 18. diameter 5 9.4 in.

19. radius 5 100 m 20. radius 5 65 mi

21. diameter 5 10}12

} in. 22. diameter 5 8.5 cm

22}7

NAME ________________________________________ DATE ______________ PERIOD _____

4 in. 15 cm

8 ft21 m

16 km

37 mm


Less

on

6–9

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems


1. PLATES A manufacturing company is

producing dinner plates with a

diameter of 12 inches. They plan to put

a gold edge on each plate. Determine

how much gold edging they need for

each plate by finding the circumference

of each plate. Round to the nearest

tenth.

2. MONEY A dime has a radius of 8}12

}

millimeters. Find the circumference of

a dime to the nearest tenth.

3. MERRY-GO-ROUND Mr. Osterhout is

putting trim around the edge of a

circular merry-go-round that has a

diameter of 15 feet. How much trim

does he need to buy to the nearest

tenth?

4. PIZZA Find the circumference of a pizza

with a diameter of 10 inches. Round to

the nearest tenth.

5. RACING A circular racetrack has a

diameter of }12

} mile. How far does a car

travel in one lap around the track?

Round to the nearest tenth.

6. TIRE A bicycle tire has a radius of 15

inches. What is the circumference of

the tire? Round to the nearest tenth.

7. EQUATOR Earth’s diameter at the

equator is 7,926 miles. Find the

distance around Earth at its equator to

the nearest tenth.

8. SATURN The ring system around

Saturn has a diameter of 170,000

miles. Find the circumference of the

ring system.


Find the area of the circle.

A 5 pr2 Area of circle

A 5 p ? 52 Replace r with 5.

5 78.53981634

The area of the circle is approximately 78.5 square centimeters.

Find the area of a circle that has a diameter of 9.4 millimeters.

A 5 pr2 Area of a circle

A 5 p ? 4.72 Replace r with 9.4 4 2 or 4.7.

A < 69.4 Use a calculator.

The area of the circle is approximately 69.4 square millimeters.

Find the area of each circle. Round to the nearest tenth.

1. 2. 3.

4. radius 5 2.6 cm 5. radius 5 14.3 in. 6. diameter 5 5}12

} yd

7. diameter 5 4}3

4} mi 8. diameter 5 7.9 mm 9. radius 5 2}

15

} ft

12 ft

25 mm7 in.

ENTER

3p

5 cm

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention

Area of Circles

The area A of a circle equals the product of pi (p) and the square of its radius r.

A 5 pr 2

Less

on

11–6


Find the area of each circle. Round to the nearest tenth.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. radius 5 5.7 mm 12. radius 5 8.2 ft

13. diameter 5 3}14

} in. 14. diameter 5 15.6 cm

15. radius 5 1.1 in. 16. diameter 5 12}34

} yd

11.9 ft2.1 mm

22.5 in.

4.7 yd

8 cm4.3 ft

14 in.35 mm

4 yd

1 cm

Practice: Skills

Area of Circles

NAME ________________________________________ DATE ______________ PERIOD _____

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word Problems

Area of Circles


1. POOLS Susan designed a circular pool

with a diameter of 25 meters. What is

the area of the bottom of the pool?


2. MONEY Find the area of the coin to the

nearest tenth.

19 mm

3. DRUMS What is the area of the

drumhead on the drum shown below?


14 in.

4. PIZZA Estimate the area of the top of a

round pizza that has a diameter of

16 inches. Round to the nearest tenth.

5. GARDENING Jane needs to buy mulch

for the garden with the dimensions

shown in the figure. For how much area

does Jane need to buy mulch? Round to

the nearest tenth.

5.5 yd

6. UTILITIES What is the area of the top

surface of a circular manhole cover that

has a radius of 30 centimeters? Round

to the nearest tenth.

perimeter of quadrilaterals & triangles p = 4s

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