slicing and 3 dicing - kyrene school districtlesson 3: slicing and dicing • m1-31 area of a kite a...

LESSON 3: Slicing and Dicing • M1-29

WARM UPUse a formula to determine the area of each fi gure.

1.

22 m

10.5 m

2.

11 cm

7 cm

3.

65 yd

35 yd

30 yd

LEARNING GOALS• Decompose composite

geometric figures into rectangles, parallelograms, and/or triangles to determine their areas.

• Solve real-world problems by decomposing shapes into triangles and rectangles.

KEY TERM• kite

Slicing and DicingComposite Figures

3

You know how to calculate the area of triangles, rectangles, parallelograms, and trapezoids. How can you use what you know about the areas of these shapes to determine areas of more complex shapes?

C01_SE_M01_T01_L03.indd 29C01_SE_M01_T01_L03.indd 29 29/03/17 8:05 AM29/03/17 8:05 AM

M1-30 • TOPIC 1: Factors and Area

Getting Started

Let Me Count the Ways

To calculate the total area of an oddly-shaped region, one strategy is to divide the region into smaller familiar regions and then calculate the area of each familiar region.

1. Draw lines in each fi gure to divide the fi gure into smaller familiar shapes. Then name the familiar shapes that make up the total fi gure.

a.

b.



Area of a Kite

A kite is a quadrilateral with two pairs of consecutive congruent sides where opposite sides are not congruent.

1.7 cm

4.1 cm

4.1 cm

C

B

A

D

1.7 cm

The area of a kite, like that of other quadrilaterals, can be determined by decomposing its shape into smaller familiar shapes.

Mr. Gram sketched the kite shown. He asked his students to add a line segment that would divide the kite into two familiar fi gures.

1.7 cm

4.1 cm

4.1 cm

C

B

A

D

1.7 cm

Molly’s kite

1.7 cm

4.1 cm

4.1 cm

C

B

A

D

1.7 cm

James’s kite

1. Describe each student’s strategy and identify any additional information you would need to calculate the area. Would you rather use Molly’s or James’s diagram to compute the area of the kite?

ACTIVIT Y

3.1

So, it can't just look like a kite. In mathematics, kite has a very specific definition.



2. Use the information given to calculate the area of the kite using both Molly’s and James’s strategies.

Given: AC 5 5 cm BD 5 2.5 cm AE 5 1.1 cm BE 5 1.25 cm CE 5 3.9 cm DE 5 1.25 cm

Kite ABCD

1.7 cm

4.1 cm

4.1 cm

CE

B

A

D

1.7 cm

3. Which method do you prefer for Question 2, Molly’s or James’s method? Why?

We use capital letters to describe a line segment. The letters AC indicate the length of the line segment that goes from the point at A to the point at C.



Area of Complex FiguresACTIVIT Y

3.2

Decompose the composite shape in each image into parallelograms, triangles, and/or trapezoids to calculate the approximate area of each. Show your work.

1. Suppose a gallon of paint covers about 400 square feet. How much paint would you need to paint the entire back of this house?

50 ft

9 ft

18 ft

12 ft

10 ft

2. Suppose that carpeting costs $1.20 per square foot. How much would it cost to carpet every room in this house except the kitchen?

DiningroomKitchen

Livingroom

Enclosed porch

10 feet

10 feet

10 feet

5 feet

35 feet

8 feet

14 feet

12 feet



3. Estimate the area of France.

SPAIN

Bay ofBiscay

Mediterranean Sea

Ligurian Sea

ITALY

SWITZERLAND

GERMANYBELGIUM

PARIS

U.K.

0 35 75 mi

FRANCE

4. Estimate the area of Namibia.

N

ATLANTICOCEAN

BOTSWANA

ZAMBIA

ZAMBABWE

ANGOLA

SOUTH AFRICA

NAMIBIA

0 50 100 mi

Windhoek

NAMIBIA



5. The fi gure shown is composed of a rectangle and four congruent trapezoids. Determine the area of the shaded region.

30 cm

22 cm 80 cm

T

C

R

E

6. The fi gure shown is composed of a rectangle and a hexagon. The length of each side of the hexagon is 2 centimeters. Determine the area of the shaded region.

4

3.5

2 cm



NOTESTALK the TALK

Use Your Powers of Mathematical Reasoning

1. Determine the area of the shaded triangle inside the square. Explain your strategy.

2. Create a presentation of your solution strategy for the class.

10 in.

3 in.

3 in.

10 in

.


Assignment

WriteDefi ne composite fi gure and

draw a picture of an example.

RememberThe area of a composite fi gure can be determined by decomposing

it into familiar shapes and then adding together the areas of those

shapes.

Practice1. Calculate the area of the composite fi gure.

20 in.

7 in.7 in.

3. In the given kite, AE 5 6 ft, CE 5 6 ft, BE 5 9 ft,

and DE 5 15 ft. Determine the area of the kite.

DE

C

B

A

2. A city wants to create a garden according to the

plan below. Calculate the area of the garden.

4. In the given kite, SZ 5 10 yards, WZ 5 10 yards,

TZ 5 12 yards, and RZ 5 32 yards. Determine

the area of the kite.

RZ

W

T

S

8 m

6 m 12 m

12 m

4 m

5 m 3 m

5 m

4 m

8 m

10 m




Review1. A patio is built in the shape of a trapezoid, as shown. Determine the area of the patio.

15 ft

6 ft

8 ft

2. Calculate the area of the given triangle.

4.5 m

4 m

3. Calculate the area of the given parallelogram.

20 ft

4.5 ft

4. Determine the area of a square picture that has a side length of 14 cm.

5. Use the Distributive Property to write an equivalent addition expression for 5(17 1 20).

StretchCalculate the area of each shaded region.

1. The fi gure is composed of 2 kites.

Given: MR 5 RS 5 5 feet, ST 5 PT 5 10 feet,

and NS 5 QS 5 12 feet.

N

Q

PMR S T

2. The fi gure is composed of 2 congruent triangles

and a rhombus.

5 in.

4 in.

4 in.

4 in.


slicing and 3 dicing - kyrene school districtlesson 3: slicing and dicing • m1-31 area of a kite a...

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