Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then...

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Transcript of Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then...

Page 1: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
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Page 2: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Name and Classify Polygons

A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

There are 4 sides, so this is a quadrilateral.

No line containing any of the sides will pass through the

interior of the quadrilateral, so it is convex.

The sides are not congruent, so it is irregular.Answer: quadrilateral, convex, irregular

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Page 3: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Name and Classify Polygons

B. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

There are 9 sides, so this is a nonagon.

A line containing some of the sides will pass through the interior of the nonagon, so it is concave.

Since the polygon is concave, it must be irregular.

Answer: nonagon, concave, irregular

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Page 4: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
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Page 5: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Find Perimeter and Area

A. Find the perimeter and area of the figure.

P = 2ℓ + 2w Perimeter of a rectangle

= 2(4.6) + 2(2.3) ℓ = 4.6, w = 2.3

= 13.8 Simplify.

Answer: The perimeter of the rectangle is 13.8 cm.

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Page 6: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Find Perimeter and Area

A. Find the perimeter and area of the figure.

A = ℓw Area of a rectangle

Answer: The area of the rectangle is about 10.6 cm2.

= (4.6)(2.3) ℓ = 4.6, w = 2.3

= 10.58 Simplify.

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Page 7: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Find Perimeter and Area

B. Find the circumference and area of the figure.

≈ 25.1 Use a calculator.

Answer: The circumference of the circle is about 25.1 inches.

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Page 8: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Find Perimeter and Area

B. Find the circumference and area of the figure.

≈ 50.3 Use a calculator.

Answer: The area of the circle is about 50.3 square inches.

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Page 9: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).

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Page 10: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

Step 1

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Page 11: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

The perimeter of pentagon ABCDE is 5.7 + 4.1 + 6 + 5 + 4.2 or about 25 units.

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Page 12: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

Step 2

Divide the pentagon into two triangles and a rectangle.

Find the area of the triangles.

Area of Triangle 1

Area of a triangle

Substitute.

Simplify.

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Page 13: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

Substitute.

Simplify.

Area of Triangle 2

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Page 14: Concept. Example 1 Name and Classify Polygons A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

Perimeter and Area on the Coordinate Plane

Find the area of the rectangle.

Area of a rectangle

Substitute.

Simplify.

The area of pentagon ABCDE is 9 + 2.5 + 30 or 41.5 square units.

Answer: The perimeter is about 25 units and the area is 41.5 square units.

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