Multiple choice

A girl wants to construct a circular swimming pool in her house which is in the shape of a trapezium. The lengths of the oblique sides of the house plot (in trapezium shape) are 26 m and 30 m. If the radius of the biggest circle that can be marked for the swimming pool is 12 m, then what must be the minimum area (in sq.m) of the plot?

  1. 336

  2. 672

  3. 728

  4. 1344

  5. 934
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of the inscribed circle in a trapezium is related to the height. If the radius is 12, the height h = 24. For a tangential trapezium, the sum of opposite sides is equal. Sum of parallel sides = Sum of oblique sides = 26 + 30 = 56. Area = 0.5 * (sum of parallel sides) * height = 0.5 * 56 * 24 = 672.

AI explanation

For the biggest circle to fit inside the trapezium with a radius of 12 m, the sum of the parallel sides must equal the sum of the oblique sides, making the sum of the parallel sides 26 m plus 30 m, which equals 56 m. Using the area of a trapezium formula, half the height times the sum of the parallel sides, the area is half of 24 times 56, equaling 672 square meters. The minimum area of the plot is 672 square meters.

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