Multiple choice

Directions : Select the correct alternative from the given choices. Raghu wants to construct a circular swimming pool in his plot which is in the shape of a trapezium. The lengths of the oblique sides of the plot are 26 m and 30 m. lf the radius of the biggest circle that can be marked for the pool is 12 m, what must be the minimum area (in sq.m) of the plot?

  1. 336

  2. 672

  3. 728

  4. 1344
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The circle is inscribed in the trapezium. The height of the trapezium is the diameter of the circle, which is 24 m. Using the properties of a tangential trapezium, the area can be calculated.

AI explanation

Since the biggest inscribed circle has a radius of 12 m, the height of the trapezoidal plot must be 24 m. The area of a trapezium is calculated as (1/2)height(sum of parallel sides), so the sum of the parallel sides must equal (2*Area)/24. To find the minimum area, the parallel sides must be as short as possible, meaning they exactly equal the oblique sides of 26 m and 30 m; thus, the area is (1/2)24(26+30) = 672 sq. m.

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