Perimeter of a Triangle

4 Key excerpts on "Perimeter of a Triangle"

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  eBook - ePub

  Common Mistakes in Teaching Elementary Math—And How to Avoid Them

  • Fuchang Liu(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  After giving her children the definition of the perimeter of a polygon, Jane started with the polygon of the fewest sides: the triangle. She told them that to find the Perimeter of a Triangle, what they needed to do was add up the lengths of its three sides. For practice, she listed a few triangles, each with three numbers indicating the lengths of its three sides. For the last triangle, she said, “This triangle has three sides with lengths of 7, 13, and 5 centimeters. What’s its perimeter?”

  Few people would make a mistake on the sum of the three angle measures of a triangle. For example, if one of Jane’s children said to her that he had a triangle with angle measures of 50°, 50°, and 90°, Jane would immediately tell him that it’s impossible to have such a triangle because in plane geometry, the sum of the three angle measures in any triangle is always 180°. But Jane was not aware that there is a restriction on the lengths of a triangle’s three sides as well, as expressed in the triangle inequality theorem. Simply put, this theorem states that in any triangle, the sum of any two sides is greater than the third. Conversely, any one side of a triangle is shorter than the sum of the two other sides. Applied to a daily-life situation, this theorem can explain why a shortcut is shorter. Suppose you are at point A going to point C through point B, as shown in Figure 10.10 , you will find going from A to C directly through the lawn is shorter—because the shortcut involves one side of this triangle whereas going from A to B and then to C involves the sum of the other two sides.

  Jane’s mistake of enumerating the lengths of the three sides of a triangle as being 7, 13, and 5 centimeters would immediately become apparent if she attempted to draw such a triangle to scale. We can make this attempt for her here. Let’s designate the three sides having lengths of 7, 13, and 5 centimeters as sides a, b , and c , respectively. First, using actual measures, let’s draw side b (13 cm, the longest side) on a piece of graph paper. At one endpoint of side b let’s draw side a (7 cm) as close to it as possible. Next, at the other endpoint of b , let’s draw side c (5 cm), also as close to it as possible (see Figure 10.11 ). We can easily see that no matter how close sides a and c are to side b , their endpoints won’t join each other to make a triangle. In other words, a and c added together must be longer than b

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  GED® Math Test Tutor, For the 2014 GED® Test

  • Sandra Rush(Author)
  • 2013(Publication Date)
  • Research & Education Association

    (Publisher)

  p) is given by

  The area of a triangle is one-half the base times the height of the triangle. You can choose any of the three sides to be the base, although for an isosceles triangle it is easiest if it is the unequal side, and for a right triangle it should be one of the legs. The height is the perpendicular distance from the base to the opposite angle.

  This is the tricky part: finding the height of a triangle. It is one of the sides only if the triangle is a right triangle because the two legs are perpendicular. So for any other triangle, remember that it is not one of the other sides. In fact, for an obtuse triangle, the height could be a measurement outside the triangle itself.

  The formula for the area (A) of a triangle, where b is the base and h is the height to that base, is

  Where did the come in? For any triangle, we can duplicate it across any side and we will end up with a four-sided figure in which the sides across from each other are equal. We will see shortly that the area of this new four-sided figure (called a parallelogram) is simply its base times its height (or length times width). The two triangles are identical. The area of either triangle is one-half the area of the four-sided figure. So when you figure the area of a triangle, don’t forget the

  Even though a formula sheet is provided on the GED® test, the formulas for the perimeter and area of a triangle (and a few others) are not listed there but you are expected to know tem. At the end of this chapter is a list of the formulas you are expected to know and that don’t appear on the GED® test formula sheet but may appear on the GED®

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  Teaching Mathematics Visually and Actively

  • Tandi Clausen-May(Author)
  • 2013(Publication Date)
  • SAGE Publications Ltd

    (Publisher)

  Learners spend time drawing shapes on squared paper, and counting and recording the number of squares used (the area), and the number of units around the edge (the perimeter). But this approach focuses on the numbers – and to a visual and kinaesthetic thinker one number may be very like another, so area and perimeter are likely to get muddled. But area and perimeter are quite different concepts. Perimeter is fairly straightforward. It is the distance around a shape. I can walk around the perimeter of a large shape, or trace my pencil around the perimeter of a smaller one – so I can see and feel what a perimeter is. But area is more difficult to understand. It may be thought of as ‘an amount of flatness’. Theme: Mathematical Language – Area and Perimeter The ‘mathematical’ terms area and perimeter may become easier to remember if they are associated with appropriate movements. Area may be thought of as a ‘measure of flatness’. A common sign for area is a hand held flat above the table, and moved round in a horizontal plane as if to smooth the air underneath. A perimeter is the distance around a shape. The common sign for this uses both hands. The forefinger of the left hand is held up, and then a roughly square path is sketched out in the air with the forefinger of the right hand. In the Classroom – Tiles and Sticks Activities that relate area and perimeter to different materials may provide a firmer foundation than mere counting for the development of these concepts. Square tiles, which can be picked up and moved around, provide a better starting point for area than drawn squares. A set of sticks that are the same length as the edge of a tile provide a model of the perimeter. The challenge may then be set to surround a given number of tiles with different numbers of sticks, or to fill different spaces, each surrounded by a given number of sticks, with different numbers of tiles

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  CLEP® College Mathematics Book + Online

  • Mel Friedman(Author)
  • 2012(Publication Date)
  • Research & Education Association

    (Publisher)

  CHAPTER 6

  Geometry Topics

   

  CHAPTER 6

  GEOMETRY TOPICS

  Plane geometry refers to two-dimensional shapes (that is, shapes that can be drawn on a sheet of paper), such as triangles, parallelograms, trapezoids, and circles. Three-dimensional objects (that is, shapes with depth) are the subjects of solid geometry.

  TRIANGLES

  A closed three-sided geometric figure is called a triangle. The points of the intersection of the sides of a triangle are called the vertices of the triangle.

  A side of a triangle is a line segment whose endpoints are the vertices of two angles of the triangle. The Perimeter of a Triangle is the sum of the measures of the sides of the triangle.

  An interior angle of a triangle is an angle formed by two sides and includes the third side within its collection of points. The sum of the measures of the interior angles of a triangle is 180°.

  A scalene triangle has no equal sides.

  An isosceles triangle has at least two equal sides. The third side is called the base of the triangle, and the base angles (the angles opposite the equal sides) are equal.

  An equilateral triangle has all three sides equal. . An equilateral triangle is also equiangular, with each angle equaling 60°.

  An acute triangle has three acute angles (less than 90°).

  An obtuse triangle has one obtuse angle (greater than 90°).

  A right triangle has a right angle. The side opposite the right angle in a right triangle is called the hypotenuse of the right triangle. The other two sides are called the legs (or arms) of the right triangle. By the Pythagorean Theorem, the lengths of the three sides of a right triangle are related by the formula

  c2 = a2 + b2

  where c is the hypotenuse and a and b are the other two sides (the legs). The Pythagorean Theorem is discussed in more detail in the next section.

  An altitude, or height

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