CBSE Class 10-Mathematics: Chapter –12 Areas Related to Circles Part 25

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4 Mark Questions

Question 1:

The area of an equilateral is with each center of the triangle as vertex of circle is drawn with radius equal to half the length of the side of triangle, find the area of the shaded region.

Answer:

Area of shaded region area of (Area of sector BPR)

Let ‘a’ be the side of the equilateral

Question 2:

The given figure depicts a racing track whose left and right ends are semi-circular. The difference between the two inner parallel line segments is 60m and they are each 106m long. If the track is 10m wide, find:

(i) The distance around the track along its inner edge,

(ii) The area of the track.

Answer:

(i) The distance around the track along the inner edge

(ii) The area of the track

Question 3:

Three horses are tethered with 7m long ropes at the three corners of a triangular field having sides 20m, 34m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed.

Answer:

Let

Area which can be grazed by three horses = Area of sector with central angle and radius 7 cm + Area of sector with central angle and radius 7 cm + Area of sector with central angle and radius

Sides of plot ABC are , and

Area of triangular plot

Area of

Area grazed by the horses

Ungrazed area