# Honors Geometry Companion Book, Volume 1

1.2.1 Using Formulas in Geometry (continued)

A rectangle has two pairs of equal sides. So, if the length and width of a rectangle are represented by l and w respectively, then the rectangle has two sides of length l and two sides of length w . So, the perimeter of the rectangle is l + l + w + w . Or, multiplication and addition can be used to find the perimeter of the rectangle. P = l + l + w + w = 2 l + 2 w The area of a rectangle can be found by multiplying the length by the width. The perimeter of a square can also be found by using multiplication because all four sides of a square are always equal. The area of a square can be found by multiplying the length by the width. However, the length and width of a square are always equal and so the two dimensions can be represented by the same variable. A = ( s )( s ) = s 2 The perimeter of a triangle is found by adding the lengths of the three sides. The area of a triangle is found by taking one half of the product of the base and height. The figure in this example is a rectangle with length 3 cm and height 11 cm. Note that the width of a rectangle can also be referred to as the rectangle’s height and the length of a rectangle can also be referred to as the rectangle’s base. Substitute the given dimensions, 3 cm and 11 cm, into the formula for the perimeter of a rectangle and simplify to find the perimeter of the rectangle. To find the area, multiply the given dimensions. Since area is measured in square units, the units for the area of this rectangle are cm 2 .

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