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Area of a Triangle Figure 1-7 shows a triangle consisting of one-half of the rectangle shown in figure 1-6. It is obvious that the area of this triangle must equal one-half of the area of the corresponding rectangle, and the fact that it does can be demonstrated by geometrical proof. Therefore, since the formula for the area of the rectangle is A = bh, it follows that the formula for the triangle is A = 1/2bh. The triangle shown in figure 1-7, because it is half of a corresponding rectangle, contains a right angle, and is therefore called a right triangle. In a right triangle the dimension h corresponds to the length of one of the sides. The triangle shown in figure 1-8, however, is a scalene triangle, so-called because no two sides are equal. Classification of triangles will be discussed later in this chapter. Now, a perpendicular CD drawn from the apex of the triangle (from angle C) divides the triangle into two right triangles, DADC and DBDC. The area of the whole triangle equals the sum of the areas of DADC and DBDC. The area of DADC equals 1/2 (AD)(DC), and the area of DBDC equals 1/2(DB)(DC). Therefore, the area of the whole triangle equals
But since AD + DB = AB, it follows that the area of the whole triangle equals
Figure 1-8.-Triangle. The length of AB is called the base (b), and the length of DC, the altitude (h); therefore, your for-mula for determining the area of an oblique triangle is again A = 1/2bh. You must remember that in a right triangle h corresponds to the length of one of the sides, while in an oblique triangle it does not. Therefore, for a right triangle with the length of the sides given, you can determine the area by the formula A = 1/2bh. For an oblique triangle with the length of the sides given, you cannot use this formula unless you can determine the value of h, Later in this chapter you will learn trigonometric methods of determining areas of various forms of triangles on the basis of the length of the sides alone. |
 
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