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# Fig. 12.26 depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :

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

(ii) the area of the track.

**Solution:**

We are given the following information:

(i) A racing track whose right and left ends are semicircular.

(ii) The distance between the 2 inner parallel line segments is 60 m and they are 106 m long.

(iii) Width of track = 10 m

Radii of the inner semicircles HIJ and KLG (r₁) = 60/2 = 30 m

Radii of the outer semicircles BCD and EFA = 30 m + 10 m = 40 m

JK = GH = 106 m

DJ = HB = 10 m

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

= GH + arc HIJ + JK + arc KLG

= 106 + 2πr₁/2 + 106 + 2πr₁/2

= 106 + π × 30 + 106 + π × 30

= 212 + 1320/7

= (1484 + 1320)/7

= 2804/7 m

(ii) Radius of semicircle BCD = Radius of semicircle EFA

(r₂) = 30 m + 10 = 40 m

Area of the track = Area of rectangle ABHG + Area of rectange KJDE + (Area of semicircle BCD - Area of semicircle HIJ) + (Area of semicircle EFA - Area of semicircle KLG)

= {(106 × 10) + (106 × 10) + [1/2π (40)² - 1/2π (30)²]^{ }+ [1/2π (40)² - 1/2π (30)²]}

= {1060^{ }+ 1060 + [1/2π (1600 - 900)] + [1/2π (1600 - 900)] }

= 1060 + 1060 + π/2 × 700 + π/2 × 700

= 2120 + 700π)

= 2120 + 700 × 22/7

= 2120^{ }+ 2200

= 4320 m^{2}

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 12

**Video Solution:**

## Fig. 12.26 depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find : (i) the distance around the track along its inner edge (ii) the area of the track.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.3 Question 8

**Summary:**

The given figure depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, (i) the distance around the track along its inner edge is 2804/7 m and (ii) the area of the track is 4320 m^{2}.

**☛ Related Questions:**

- In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
- The area of an equilateral triangle ABC is 17320.5 cm2 . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205)
- On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.
- In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the(i) quadrant OACB,(ii) shaded region

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