13.4: Math Models and Geometry

We are surrounded by all sorts of geometry. Architects use geometry to design buildings. Artists create vivid images out of colorful geometric shapes. Street signs, automobiles, and product packaging all take advantage of geometric properties. In this chapter, we will begin by considering a formal approach to solving problems and use it to solve a variety of common problems, including making decisions about money. Then we will explore geometry and relate it to everyday situations, using the problem-solving strategy we develop.

• 13.4.1: Solve Money Applications

  Solving coin word problems is much like solving any other word problem. However, what makes them unique is that you have to find the total value of the coins instead of just the total number of coins. For coins of the same type, the total value can be found by multiplying the number of coins by the value of an individual coin. You may find it helpful to put all the numbers into a table to make sure they check.

• 13.4.2: Use Properties of Angles, Triangles, and the Pythagorean Theorem (Part 1)

  An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle and the common endpoint is called the vertex. If the sum of the measures of two angles is 180°, then they are supplementary angles. But if their sum is 90°, then they are complementary angles. We will adapt our Problem Solving Strategy for Geometry Applications. Since these applications will involve geometric shapes, it will help to draw a figure and label it with the information from the problem.

• 13.4.3: Use Properties of Angles, Triangles, and the Pythagorean Theorem (Part 2)

  Triangles are named by their vertices. For any triangle, the sum of the measures of the angles is 180°. Some triangles have special names such as the right triangle which has one 90° angle. The Pythagorean Theorem tells how the lengths of the three sides of a right triangle relate to each other. It states that in any right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. To solve problems that use the Pythagorean Theorem, we will need to find square roots.

• 13.4.4: Use Properties of Rectangles, Triangles, and Trapezoids (Part 1)

  Many geometry applications will involve finding the perimeter or the area of a figure. The perimeter is a measure of the distance around a figure. The area is a measure of the surface covered by a figure. The volume is a measure of the amount of space occupied by a figure. A rectangle has four sides and four right angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, L, and the adjacent side as the width, W.

• 13.4.5: Use Properties of Rectangles, Triangles, and Trapezoids (Part 2)

  Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of a triangle is one-half the base times the height. An isosceles triangle is a triangle with two sides of equal length is while a triangle that has three sides of equal length is an equilateral triangle. A trapezoid is four-sided figure with two sides that are parallel, the bases, and two sides that are not. The area of a trapezoid is one-half the height times the sum of the bases.

Figure 9.1 - Note the many individual shapes in this building. (credit: Bert Kaufmann, Flickr)

Contributors

• Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."