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Presentation transcript:

Concept

There are 4 sides, so this is a quadrilateral. 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 Example 1

There are 9 sides, so this is a nonagon. 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 Example 1

Concept

A. Find the perimeter and area of the figure. 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. Example 2

A. Find the perimeter and area of the figure. Find Perimeter and Area A. Find the perimeter and area of the figure. A = ℓw Area of a rectangle = (4.6)(2.3) ℓ = 4.6, w = 2.3 = 10.58 Simplify. Answer: The area of the rectangle is about 10.6 cm2. Example 2

B. Find the circumference and area of the figure. 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. Example 2

B. Find the circumference and area of the figure. 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. Example 2

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). Example 4

Perimeter and Area on the Coordinate Plane Step 1 Example 4

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. Example 4

Divide the pentagon into two triangles and a rectangle. 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. Example 4

Area of Triangle 2 Substitute. Simplify. Perimeter and Area on the Coordinate Plane Area of Triangle 2 Substitute. Simplify. Example 4

Find the area of the rectangle. 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. Example 4