(a) A standard sheet of paper measures 8 1/2 by 13 inches. Find the area of one such sheet of paper in m2.8.5(!meter/39.37in) — 0.2159 13 (!meter/39.37in ) — 0.3302 0.2159 X 0.3302 = 0.0713 = 0.0713 m2 (b) A second sheet of paper is three-quarters as long and three-quarters as wide as the one described in part (a). By what factor is its area less than the area found in part(a)?= times less

a)    A = 0.07129 m²

b)    A / A ’= 1.77

Explanation:

In this exercise we are asked to find the area in SI units, so let's start by reducing the dimensions to SI units.

width a = 8.5 inch (2.54 cm 1 inch) (1 m / 100 cm)

            a = 0.2159 m

length l = 13 inch (2.54 cm / 1 inch) (1 m / 100 cm)

              l = 0.3302 m

The area of a rectangle is

            A = l a

             A = 0.3302 0.2159

             A = 0.07129 m²

b) we have a second sheet with reduced dimensions

         a ’= 3/4 a

         l ’= ¾ l

Let's find the area of this glossy sheet

         A ’= l’ a ’

         A ’= ¾ l ¾ a

         A ’= 9/16 l a

To find the factor we divide the two quantities

           A / A ’= l a 16 / (9 l a

            A / A ’= 1.77