 # Polygons, Circles, and Solids

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Polygons, Circles, and Solids
Section 2.3 Polygons, Circles, and Solids

Common Polygons

Triangles

Sum of Interior angles of Regular Polygon
Interior sum of angles of regular polygon is (n-2)180, n is the number of sides What is the measure of the interior angles of a STOP sign? 1080 degree.

A rectangle has four sides that meet to form 90° angles
A rectangle has four sides that meet to form 90° angles. Each set of opposite sides is parallel and congruent (has the same length). 90° angles In a rectangle, if one right angle is shown, the other three are also right angles. 5 cm 9 cm Each longer side of a rectangle is called the length (l) and each shorter side is called the width (w). Slide

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Finding the Perimeter of a Rectangle
Parallel Example 1 Finding the Perimeter of a Rectangle Find the perimeter of each rectangle. a. 6 m 16 m P = 2 • l • w P = 2 • 16 m • 6 m P = m m P = 44 m The perimeter of the rectangle is 44 m. Slide

Finding the Perimeter of a Rectangle
Parallel Example 1 continued Finding the Perimeter of a Rectangle Find the perimeter of each rectangle. b. A rectangle 7.8 ft by 12.3 ft P = 2 • l • w P = 2 • 12.3 ft • 7.8 ft P = ft ft P = ft Or, you can add up the lengths of the four sides. P = ft ft ft ft P = ft Either method will give you the same result. Slide

The perimeter of a rectangle is the distance around the outside edges.
The area of a rectangle is the amount of surface inside the rectangle. 1 m 1 square meter or (m)2 8 m 5 m We have five rows of eight square meters for a total of 40 square meters. Slide

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Other sizes of squares that are often used to measure area:
Squares of many sizes can be used to measure area. For smaller areas, you might use the ones shown below. (Approximate-size drawings) 1 square inch (1 in.2) 1 in. 1 square centimeter (1 cm2) 1 cm 1 square millimeter (1 mm2) 1 mm Other sizes of squares that are often used to measure area: 1 square meter (1 m2) 1 square foot (1 ft2) 1 square kilometer (1 km2) 1 square yard (1 yd2) 1 square mile (1 mi2) Slide

Finding the Area of a Rectangle
Parallel Example 2 Finding the Area of a Rectangle Find the area of each rectangle. a. 7 yd 15 yd A = l • w A = 15 yd • 7 yd A = 105 yd2 Slide

Finding the Area of a Rectangle
Parallel Example 2 continued Finding the Area of a Rectangle Find the area of each rectangle. b. 18 cm 3 cm A = l • w A = 18 cm • 3 cm A = 54 cm2 Slide

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Finding the Perimeter and Area of a Square
Parallel Example 3 Finding the Perimeter and Area of a Square a. Find the perimeter of a square where each side measures 7 m. Use the formula. Or add up the four sides. P = 4 • s P = 7 m + 7 m + 7 m + 7 m P = 4 • 7 m P = 28 m P = 28 m Same answer Slide

Finding the Perimeter and Area of a Square
Parallel Example 3 continued Finding the Perimeter and Area of a Square b. Find the area of a square where each side measures 7 m. A = s2 A = s • s A = 7 m • 7 m A = 49 m2 Square units for area. Slide

Finding the Perimeter and Area of a Composite Figure
Parallel Example 4 Finding the Perimeter and Area of a Composite Figure a. The floor of a room has the shape shown. 6 ft 30 ft 21 ft 24 ft 15 ft Suppose you want to put new wallpaper border along the top of the walls. How much material do you need? Find the perimeter of the room by adding up the length of the sides. P = 30 ft + 21 ft + 24 ft + 15 ft + 6 ft + 6 ft = 102 ft Slide

Finding the Perimeter and Area of a Composite Figure
Parallel Example 4 continued Finding the Perimeter and Area of a Composite Figure b. The carpet you like cost \$24.25 per square feet. How much will it cost to carpet the room? 6 ft 30 ft 21 ft 24 ft 15 ft Slide

Finding the Perimeter and Area of a Composite Figure
Parallel Example 4 continued Finding the Perimeter and Area of a Composite Figure Finally, multiply to find the cost of the carpet. 36+504= 540 sq feet. 6 ft 21 ft 24 ft Slide

A parallelogram is a four-sided figure with opposite sides parallel, such as the ones below. Notice that the opposite sides have the same length. Slide

Finding the Perimeter of a Parallelogram
Example 1 Finding the Perimeter of a Parallelogram Find the perimeter of a the parallelogram. 15 cm 9 cm P = 15 cm + 9 cm + 15 cm + 9 cm = 48 cm Slide

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Finding the Area of a Parallelogram
Example 2 Finding the Area of a Parallelogram Find the area of the parallelogram. 10 m 4 m 3 m 4 m 10 m The base is 10 m and the height is 3 m. Use the formula to solve. A = b ∙ h A = 10 m ∙ 3 m A = 30 m2 Slide

A triangle is a figure with exactly three sides
A triangle is a figure with exactly three sides. To find the perimeter of a triangle, add the lengths of the three sides.

Finding the Perimeter of a Triangle
Parallel Example 1 Finding the Perimeter of a Triangle Find the perimeter of the triangle. P = 12 ft + 16 ft + 20 ft = 48 ft 20 ft 12 ft 16 ft

Pythagorean Theorem 𝑎 2 + 𝑏 2 = 𝑐 2 it only works on Right Triangles.
Where a and b are legs and c is the hypotenuse.

The height of a triangle is the distance from one vertex of the triangle to the opposite side (base). The height line must be perpendicular to the base; that is, it must form a right angle with the base.

Find the Area of a Triangle
Parallel Example 2 Find the Area of a Triangle Find the area of each triangle. a.

Find the Area of a Triangle
Parallel Example 2 continued Find the Area of a Triangle Find the area of each triangle. c.

r d Slide

Finding the Diameter and Radius of a Circle
Parallel Example 1 Finding the Diameter and Radius of a Circle Find the unknown length of the diameter or radius in each circle. a. Because the radius is 12 in., the diameter is twice as long. r = 12 in. d = ? d = 2 • r d = 2 • 12 in. d = 24 in. Slide

Finding the Diameter and Radius of a Circle
Parallel Example 1 continued Finding the Diameter and Radius of a Circle Find the unknown length of the diameter or radius in each circle. b. The radius is half the diameter. r = d 2 r = ? d = 7 m r = 7 m 2 1 2 r = 3.5 m or m Slide

The perimeter of a circle is called its circumference.
Circumference is the distance around the edge of a circle. Slide

Dividing the circumference of any circle by its diameter
always gives an answer close to 3.14. This means that going around the edge of any circle is a little more than 3 times as far as going straight across the circle. This ratio of circumference to diameter is called Slide

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Finding the Circumference of Circles
Parallel Example 2 Finding the Circumference of Circles Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth. a. The diameter is 24 m, so use the formula with d in it. 24 m C = • d C = • m C ≈ m Rounded Slide

Finding the Circumference of Circles
Parallel Example 2 Finding the Circumference of Circles Find the circumference of each circle. Use 3.14 as the approximate value for . Round answers to the nearest tenth. In this example, the radius is labeled, so it is easier to use the formula with r in it. b. 6.5 cm C = 2 • • r C = 2 • • 6.5 cm C ≈ cm Rounded Slide

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Finding the Area of Circles
Parallel Example 3 Finding the Area of Circles Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. a. A circle with a radius of 14.2 cm. A = • r • r A ≈ • 14.2 cm • 14.2 cm A ≈ cm2 Rounded; square units for area Slide

Finding the Area of Circles
Parallel Example 3 continued Finding the Area of Circles Find the area of each circle. Use 3.14 for . Round answers to the nearest tenth. b. 24 ft First find the radius. r = d 2 r = = 12 ft 24 ft 2 Now find the area. A ≈ • 12 ft • 12 ft A ≈ ft2 Slide

HW section 2.3 13-59