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Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6.
Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6.
Areas Related to Circles | Exercise 11.3 | Maths | NCERT Exemplar
Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6.

Solution:

From the given figure,

We got that the Length and breadth of the rectangular portion (AFDC) of the flower bed are \[38\] cm and \[10\] cm respectively.

We know that,

Area of the flower bed = Area of the rectangular portion + Area of the two semi-circles.

Therefore, Area of rectangle AFDC = Length × Breadth

= \[38\times 10=380\] \[c{{m}^{2}}\]

From the fig, both ends of flower bed are semi-circle in shape.

∴ Diameter of the semi-circle is equal to breadth of the rectangle AFDC i.e., \[10\] cm

Therefore, Radius of the semi-circle = \[10/2=5\] cm

Now, Area of the semi-circle = \[\pi {{r}^{2}}/2=25\pi /2\] \[c{{m}^{2}}\]

As there are two semi-circles in the flower bed,

∴ Area of two semi-circles = \[2\times (\pi {{r}^{2}}/2)=25\pi \] \[c{{m}^{2}}\]

Therefore, Total area of flower bed = \[(380+25\pi )\] \[c{{m}^{2}}\]

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