In the shortcut method, a circle is 78.5% of the area of its circumscribed square. If the square is 20’ by 20’, the circle area is approximately:

In the shortcut method, a circle is 78.5% of the area of its circumscribed square. If the square is 20’ by 20’, the circle area is approximately:

• A. 392 sq ft
• B. 256 sq ft
• C. 400 sq ft
• D. 314 sq ft

Answer: (D)

The circle’s area is a fixed proportion of its circumscribed square’s area. For a circle inscribed in a square, the circle fits exactly inside, so the ratio of their areas is the area of a circle with diameter equal to the square’s side over the square’s area, which is pi/4. That’s about 0.785 or 78.5%, matching the given shortcut. With a 20 by 20 square, the square area is 400 square feet. Multiply by pi/4 (≈ 0.785) to get the circle area: 400 × 0.785 ≈ 314 square feet. So the circle’s area is about 314 sq ft.

The circle’s area is a fixed proportion of its circumscribed square’s area. For a circle inscribed in a square, the circle fits exactly inside, so the ratio of their areas is the area of a circle with diameter equal to the square’s side over the square’s area, which is pi/4. That’s about 0.785 or 78.5%, matching the given shortcut.

With a 20 by 20 square, the square area is 400 square feet. Multiply by pi/4 (≈ 0.785) to get the circle area: 400 × 0.785 ≈ 314 square feet. So the circle’s area is about 314 sq ft.