Course 1 Unit 9

Area

Name: _________________

__Lesson 9-1: Area of Parallelograms

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polygon – _______________________________________________________________________________________________________________________

parallelogram – __________________________________________________________________________________________________________________

rhombus – _______________________________________________________________________________________________________________________

Venn Diagram:

Example 1

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Find the area of the parallelogram. The base is 6 units, and the height is 8 units.

A = bh

A = ____ · _____

A = ______

______ square units or ______ units²

Example 2Find the area of the parallelogram.

A = bh

A = ____ · _____

A = ______

______ square units or ______ units²

Got it? Find the area of each parallelogram.

1. 2.

Finding the HeightThe formula to find the height is this…

Height = Area ÷ baseOr

Height = AreaBase

Example 3~ 3 ~

Find the missing dimension of the parallelogram.

height = area ÷ base

height = _______ ÷ _______

height = _______ inches

Got it? Find the missing dimension of the parallelogram.

3. 4.

Example 4Romilla is painting a replica of the national flag of Trinidad and Tobago for a research project. Find the area of the black stripe.

12 (634 )

634 = ¿¿

12 (274 ) =

121 · 274 = ¿¿

= _____ sq. in.

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Guided Practice:Find the area of each parallelogram.

1. 2.

3. Find the height of a parallelogram if its base is 35 centimeters and its area is 700 square centimeters.

4. What two formulas can you use when finding the height of a parallelogram?

5. What two basic shapes make up a parallelogram?

6. Draw a parallelogram with an area of 24 square inches. (There are many answers.)

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Lesson 9-2 Area of Trianglescongruent – _____________________________________________________________________________________________________________________

**They are ______________________ the same**

Example 1Find the area of the triangle.

A = 12· ______ · ______

A = 12 · ______

A = ______ units²

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Example 2Find the area of the triangle.

A = ½ bh

A = 12· ______ · ______

A = 12 · ______

A = ______ m²

Got it? Find the area of each triangle.

1. 2.

Finding the Base or Height:base = 2(Area) ÷ heightheight = 2(Area) ÷ base

Example 3Find the missing dimension of the triangle.

base = 2(Area) ÷ height

base = 2(______) ÷ _______

base = ________ ÷ _______

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base = ________ cm

Got it? Find the missing side length for each triangle.Formulas: base = 2(Area) ÷ height

height = 2(Area) ÷ base

3. 4.

Example 4The front of a camping tent has the dimensions 5ft by 3ft. How much material was used to make the front of the tent?

A = 12(______)(______)

A = 12(______)

A = _______

A = ________ sq. ft.

Guided Practice: Find the area. Find the base.

1. 2.

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3. Compare and contrast the formula for a parallelogram to the formula for the area of a triangle. What do they have in common? What is different?

Lesson 9-3: Area of Trapezoids

Example 1Find the area of the trapezoid.

A =(b1+b2)h

2

A =(5+12)72

A = (¿¿)72

A = ¿¿

2

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A = ________ in²

Example 2:Find the area of the trapezoid.

A =(b1+b2)h

2

A =(7+12)9.82

A = (¿¿)9.82

A = ¿¿

2

A = ________ in²

Got it? 1. 2. 3.

To Find the Height…The formula for finding the height is

h=2(Area)b1+b2

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Or

h=2 (Area )÷(b1+b2)

Example 3The trapezoid has an area of 108 square feet. Find the height.

h=2 (Area )÷(b1+b2)

h=2 (¿¿ )÷ ¿

h=¿¿

h=¿¿

Got it? 4. A = 24cm²

b1= 4cmb2 = 12cm

h = ?

5. A = 21yd²b1= 2ydb2 = 5yd

h = ?

Example 4The shape of Osceola County, Florida, resembles a trapezoid. Find the approximate area of this county.

A =(b1+b2)h

2

A = (48+16)512

A =(¿¿)¿2

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A = ¿¿

2¿

A = ________ miles²

Guided Practice:Find the area of the trapezoid. Find the height of the trapezoid.

1. 2. Area = 15 square feet

base 1 = 4 feet

base 2 = 6 feet

height = ?

3. Compare and contrast the formula for a parallelogram to the formula for the area of a trapezoid. What do they have in common? What is different?

Lesson 9-4 Changes in Dimension

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Example 1Suppose the side lengths of the parallelogram at the right are tripled.What effects would this have on the perimeter?

Side A Side B Perimeter3 4 3 + 3 + 4 + 4 = 14 inches

Tripled (Multiplied by 3)

_______ ÷ 14 = _______

The perimeter is _______ times bigger.

Got it? 1. Suppose the side lengths of the trapezoid at the right are multiplied by

12. What

effect would this have on the perimeter? Top Side Bottom Perimeter

Halved (Multiplied by ½)

_______ ÷ _______ = _______

The perimeter is _______ times bigger.

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Example 2The side lengths of the triangle at the right are multiplied by 5. What effect would this have on the area?

Base Height Area

2 1A = ½ (2)(1)

= 1 cm2

Multiplied by 5

_______ ÷ 1 = _______

The area is _______ times bigger.

Got it? 2. A rectangle measures 2 feet by 4 feet. Suppose the side lengths are multiplied by 2.5. What effect would this have on the area?

Base Height Area

Multiplied by 2.5

_______ ÷ ________ = _______

The area is _______ times bigger.

Example 3

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A stop sign is in the shape of a regular octagon. Sign A shown at the right has an area of 309 square inches. What is the area of sign B?

Since 12 ÷ 8= _______

The area is 309(_______²).

309 (______) =

____________ in²

Got it? 3. Different sizes of regular hexagons are used in a quilt. Each small hexagon has side lengths of 4 inches and an area of 41.6 square inches. Each large hexagon has side lengths of 8 inches. What is the area of each large hexagon?

Hint: 8 ÷ 4 = 2, so the large is twice as big as the small.

Guided Practice:1. Each side length is doubled.

Describe the change in perimeter.

Base Height Perimeter

Multiplied by ______

2. Each side length is tripled. Describe the change in area.

Base Height Area

Multiplied by ______

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Lesson 9-5: Polygons on the Coordinate PlaneExample 1A rectangle has vertices A(2, 8), B(7, 8), C(7, 5), and D(2, 5). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.

Find the lengths of the sides, which are shown.Add up 5 + 5 + 3 + 3.

______ units

Example 2Rectangle ABCD has vertices A(2, 1), B(2, 5), C(4, 5), and D(4, 1). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.Use graph paper.

P = 2 + 2 + 4 + 4

P = ______ units

Got it? Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.

1. E(3, 6), F(3, 8), G(7, 8), H(7, 6)

2. I(1, 4), J(1, 9),

K(8, 9), L(8, 4)

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Example 3Each grid square on the zoo map has a length of 200 feet. Find the total distance, in feet, around the zoo.Find the perimeter.

10 + 7 + 7 + 3 + 3 + 4 + 4 + 4 = 42 units.

Multiply by ______ to find the total feet.

______ x ______ = __________ feet

Got it? 3. The coordinates of the vertices of a garden are (0, 1), (0, 4), (8, 4), and (8, 1). If each unit represents 12 inches, find the perimeter in inches of the garden.

Example 4Find the area of the figure in square units.The figure can be separated into a rectangle and a trapezoid.

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Area of rectangle:2 x 5 = ______ units2

Area of trapezoid:(3+4)(2)

2 = _____ units2

Total: _______ + ________ = _______ units2

Got it? 4. Find the area, in square units, of the figure.

Example 5A figure has vertices A(2, 5), B(2, 8), and C(5, 8). Graph the figure and classify it. Then find the area.

B = _____ units

H = _____ units

A = 3(3)2 = 92

or ______ units2

This figure is a _______________.

Got it? 5. Graph the figure and classify it. Then find the area. A(3, 3), B(3, 6), C(5, 6), D(8, 3)

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Guided Practice:Use the coordinates to find the length of each side. Then find the perimeter of the rectangle.

1. L(3,3), M(3,5), N(7,5), P(7,3) 2. P(3,0), Q(6,0), R(6,7), S(3,7)

3. Mrs. Piel is building a fence around the perimeter of heryard for her dog. The coordinates of the vertices of the yard are (0,0), (0,10), (5,10), and (5,0). If each grid square is has a length of 100 feet, find the amount of wire, in feet, needed for the fence.

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4. What is the shape of her yard?

Lesson 9-6: Area of Composite Figures composite figure – ________________________________________________________________________________________________________________

Example:

Example 1Find the area of the image.

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Area = 6 x 10 Area = ½ x 4 x 4

Area = _______ Area = ________

Total Area = ______ + ______ or _______ inches square

Got it? 1. 2.

Example 2Find the area of the pool’s floor.

Separate the figure into a rectangle and a trapezoid.

Rectangle: 28 x 14 = Trapezoid: (4+6)22 = 202 =

Area = ____________ Area = ____________

Total: __________ + __________ = _______________ft.2

Got it?Find the area of the figure below.3.

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Example 3Find the area of the figure at the right.Find the area of the square and the rectangle.

Square: 12(12) = _______ sq. cm.

Rectangle: 15(12) = _______ sq. cm.

Add: _______ + _______ =_______

Find the area of the overlapping section:

_______ x _______= 42 sq. cm.

Subtract: _______ – 42 = _______ sq. cm.

Got it? 4. Find the area of the figure.

Example 4Charlie and Matthew are neighbors in an apartment complex where they share the same patio. What is the area of both apartments and the patio?

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Each apartment is the same:One Apartment: 55(45) = _______

Double it: _______+ _______= _______ft2

What is the length of each side of the patio?55ft – 32ft = _______ft

Area of the patio:23(23) = _______ft2

_______– _______ = _______sq. ft.

Guided Practice:1. Why is it important to understand the formulas for area of a parallelogram, triangle, and trapezoid when finding the area of composite figures? Write your answer in complete sentences.

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