Mathematics
Perimeter of a Triangle
The perimeter of a triangle is the total distance around its three sides. To find the perimeter, you simply add the lengths of all three sides together. This measurement is important for determining the total length of fencing needed to enclose a triangular area, or for calculating the distance around any three-sided shape.
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5 Key excerpts on "Perimeter of a Triangle"
No longer available |Learn more- Daniel C. Alexander, Geralyn M. Koeberlein, , , Daniel C. Alexander, Geralyn M. Koeberlein(Authors)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
We begin this section with a reminder of the meaning of perimeter. Table 8.1 summarizes perimeter formulas for selected types of triangles, and Table 8.2 summarizes formulas for the perimeters of selected types of quadrilaterals. However, it is more important to understand the concept of perimeter than to memorize formulas. Study each figure so that you can explain its corresponding formula. Perimeter of a Polygon SemiPerimeter of a Triangle Heron’s Formula Brahmagupta’s Formula Area of a Trapezoid, a Rhombus, and a Kite Areas of Similar Polygons KEY CONCEPTS Perimeter and Area of Polygons 8.2 The outside boundary of an enclosure is called its perimeter or its periphery. Geometry in the Real World The perimeter of a polygon is the sum of the lengths of all sides of the polygon. DEFINITION Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. EXAMPLE 1 Find the perimeter of shown in Figure 8.17 if: a) in., in., and in. b) cm, cm, and SOLUTION a) b) With , is isosceles. Then is the bisector of . If , it follows that . Using the Pythagorean Theorem, we have Now . NOTE: Because , we have . We apply the perimeter concept in a more general manner in Example 2. EXAMPLE 2 While remodeling, the Gibsons have decided to replace the old woodwork with Colonial-style oak woodwork. a) Using the floor plan provided in Figure 8.18, find the amount of baseboard (in linear feet) needed for the room. Do not make any allowances for doors! b) The baseboard to be used is sold in 8-foot lengths.
eBook - PDF- Alberto D. Yazon(Author)
- 2019(Publication Date)
- Society Publishing(Publisher)
The perimeter is the length all around the outside of a polygon or the course that encircles an area. This is different from the surface area. The surface area is how much surface is being encompassed by the polygon or space (Figure 4.3). Figure 4.3: Definition of the perimeter. Source: https://upload.wikimedia.org/wikipedia/commons/9/9b/Wet_perim-eter.PNG. A perimeter is the complete boundary of the two-dimensional shape. If one wants to provide fencing all around the entire field, one needs its perimeter. For instance, if an individual wants to lay a course inside the field to keep a close observation on their field, they need its perimeter. The units of the perimeter are centimeter, meter, etc. Perimeter and Area 77 In simpler terms, the perimeter is nothing but the length of the boundary of a figure. To figure out the perimeter of a particular object, one can simply add the length of the sides, to come at its perimeter. The perimeter of a circle is basically termed as its circumference. For example: Suppose, one wraps a string around the square, the length of the string would be its perimeter. 4.4. DIFFERENCE BETWEEN AREA AND PERIME-TER The important variations between area and perimeter are being explained in detail, in the following points: • The area is being explained as the measurement of the surface of the object. Perimeter refers to the boundary that encompasses a closed figure. • Area basically projects the space being occupied by the object. Equally, perimeter indicates the outer edge or outline of the shape. • Measurement of the area is being executed in square units such as square kilometers, square feet, square inches, etc. On the contrary, the perimeter of an object or shape is being measured in linear units such as: kilometers, inches, feet, etc. • As the perimeter is being measured in linear units, it measures only one dimension that is the length of the object.
eBook - PDFMathematics
A Practical Odyssey
- David Johnson, , Thomas Mowry, , David Johnson, Thomas Mowry(Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 8.1 Perimeter and Area 539 n Polygons Two-dimensional figures can be classified by the number of sides they have. A polygon is a many-sided figure. A pentagon is a five-sided figure, a hexagon is a six-sided figure, and an octagon is an eight-sided figure. However, the names of polygons do not necessarily end with -gon . Although a three-sided figure could be called a trigon , we prefer triangle . Likewise, a four-sided figure is referred to as a quadrilateral rather than a quadragon. Our study of polygons focuses on finding the distance around a figure and the amount of space enclosed within the figure. Some of the polygons we will examine are shown in Figure 8.1. The symbol ∟ represents an angle of 90 8 (90 degrees 5 a square corner). rectangle square parallelogram trapezoid right triangle triangle Figure 8.1 Common polygons. Architect Frank Lloyd Wright used simple geometric shapes to design this stained glass window in 1911. Digital Image © The Museum of Modern Art/Licensed by SCALA/Art Resource, NY The perimeter of (or distance around) a two-dimensional figure is the sum of the lengths of its sides. As shown in Figure 8.2, the perimeter of a rect-angular scarf 18 inches wide and 2 feet long is 7 feet. (We must first convert 18 inches into 1.5 feet.) perimeter 5 distance around 5 1.5 ft 1 2 ft 1 1.5 ft 1 2 ft 5 7 ft 2 ft 2 ft 1.5 ft 1.5 ft Figure 8.2 Finding the perimeter of a rectangular scarf.
eBook - PDFIntroductory Mathematics
Concepts with Applications
- Charles P. McKeague(Author)
- 2013(Publication Date)
- XYZ Textbooks(Publisher)
A Perimeter We begin this section by reviewing the definition of a polygon, and the definition of perimeter. The most common polygons are squares, rectangles, and triangles. 11.3 ft 9.8 ft 2.6 ft 4 ft 59 ft 44 ft FIGURE 1 DEFINITION polygon A polygon is a closed geometric figure, with at least three sides, in which each side is a straight line segment. DEFINITION perimeter The perimeter of any polygon is the sum of the lengths of the sides, and it is denoted with the letter P . ©iStockphoto.com/ isitsharp 391 8.1 Perimeter and Circumference To find the perimeter of a polygon we add all the lengths of the sides together. Here are the most common polygons, along with the formula for the perimeter of each. We can justify our formulas as follows. If each side of a square is s units long, then the perimeter is found by adding all four sides together. Perimeter = P = s + s + s + s = 4s Likewise, if a rectangle has a length of l and a width of w, then to find the perimeter we add all four sides together. Perimeter = P = l + l + w + w = 2l + 2w EXAMPLE 1 Find the perimeter of the given rectangle. Solution The rectangle has a width of 5 yards and a length of 8 yards. We can use the formula for P = 2l + 2w to find the perimeter. P = 2(8) + 2(5) = 16 + 10 = 26 yards EXAMPLE 2 Find the perimeter of each of the following stamps. Write your answer as a decimal, rounded to the nearest tenth, if necessary. a. Each side is 35.0 millimeters. b. Base = 2 5 _ 8 inches, Other two sides = 1 7 _ 8 inches c. Length = 1.56 inches, Width = 0.99 inches P = 4s s Square P = 2l + 2w l Rectangle w P = a + b + c b h a c Triangle Practice Problems 1. Find the perimeter. 12 ft 7 ft 8 yd 5 yd 2. Find the perimeter of the stamps in Example 2 if they had the following dimensions. Round to the nearest tenth if necessary. a. Each side is 42 millimeters. b. Base = 3 4 _ 5 inches Other two sides = 1 2 _ 5 inches c. Length = 3.86 inches Width = 1.34 inches Answers 1. 38 ft 2.
eBook - PDFDr. Math Introduces Geometry
Learning Geometry is Easy! Just ask Dr. Math!
- (Author)
- 2004(Publication Date)
- Jossey-Bass(Publisher)
1 1 50 Dr. Math Introduces Geometry In this part, Dr. Math explains • area and perimeter • units of area • areas and perimeters of parallelograms and trapezoids Area and Perimeter We’ve talked about some of the basic shapes of geometry; now let’s look at some of their properties. Once you know how many sides a shape has, one of the first questions you might ask is: how big is it? There are two very common ways to measure size. One is area: How much space does the shape cover? If the shape were a table, how big would a tablecloth have to be to cover it without any material hang- ing over the sides? Another measure of size is perimeter: What’s the distance around the shape? If the shape were a cake, how long a squirt of icing would it take to outline the top? Dear Lorraine, The word “perimeter” means “distance around.” Think about a rec- tangle like this one: One way to walk around the rectangle would be to move from A to B (a distance of 3 feet), then from B to C (a distance of 2 feet), then from C to D (a distance of 3 feet), and finally from D to A (a distance of 2 feet). The total distance involved would be 3 ft + 2 ft + 3 ft + 2 ft, or 10 ft. So that’s the perimeter of the rectangle: 10 feet. Area is more complicated, because it involves two dimensions, whereas perimeter involves only one. The way I always think of area is in terms of the amount of paint that I would need to cover a shape. If one shape has twice as much area than another shape, I’d need twice as much paint for it. We use different measurement units for area than for perimeter. We use a linear measure for perimeter—something that measures Areas and Perimeteres of Two-Dimensional (2-D) Geometric Figures 51 Dear Dr. Math, I do not understand area and perimeter. Can you give me some idea about how they work? Thanks, Lorraine Under- standing Area and Perimeter
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