Question

The sides of a square are 16 inches in length. A new square is formed by connecting the midpoints of the sides of the original square, and two of the triangles outside the second square are shaded (see figure). Determine the area of the shaded regions (a) when this process is continued five more times, and (b) when this pattern of shading is continued infinitely. (FIGURE CANNOT COPY)

          The sides of a square are 16 inches in length. A new square is formed by connecting the midpoints of the sides of the original square, and two of the triangles outside the second square are shaded (see figure). Determine the area of the shaded regions (a) when this process is continued five more times, and (b) when this pattern of shading is continued infinitely.
(FIGURE CANNOT COPY)

Added by Shane H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Stark Ledbetter

12/03/2021

Step 1

Given that the area of the original square is 16 inches by 16 inches, the area of the shaded region after each step is a quarter of the area of the square. The sum of the geometric series after five more times is given by: \[ \frac{1}{4} \times 16 \times 16 Show more…

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The sides of a square are 16 inches in length. A new square is formed by connecting the midpoints of the sides of the original square, and two of the triangles outside the second square are shaded (see figure). Determine the area of the shaded regions (a) when this process is continued five more times, and (b) when this pattern of shading is continued infinitely. (FIGURE CANNOT COPY)