Multiple choice

Directions: A circle is inscribed in a symmetrical triangle having sides 'x'. What would be the area of the circle?

  1. 0.16x2

  2. 0.6x2

  3. 0.26x3

  4. 0.26x2

  5. 0.26x
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For an equilateral triangle with side x, the inradius r = x / (2 * sqrt(3)). The area of the circle is pi * r^2 = pi * (x^2 / 12). Using pi approx 3.14, area = 3.14 * x^2 / 12 approx 0.2616x^2.

AI explanation

A symmetrical triangle refers to an equilateral triangle, where the inradius formula is side length divided by 2 times the square root of 3. For a triangle with side x, the radius r of the inscribed circle is x divided by 2 times the square root of 3, which simplifies to x times the square root of 3 divided by 6. The area of the circle is pi times r squared, yielding pi times x squared divided by 12. Using the approximation of pi as 3.14, the area becomes 0.2617 x squared, which rounds to 0.26 x squared.

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