Question

find the area of the shaded field as shown in the figure
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Answer 1

Given:

Length of the whole field = 26 m

Breadth of the field = 12

also,

distance of the unshaded part is 4 m either sides along the breadth and 3 m on either sides along the length of the field.

therefore, we get

length of the unshaded part = 26 - (3+3) m =20 m

breadth = 12 - (4+4) = 4 m

The unshaded fig. is combination of a rectangle with hemispheres on either sides along its breadth.

Therefore, area of the unshaded region is

b × [l - 2(r)] + 2 × πr²/2

= b × [l - 2r] + πr²

To find :

Area of shaded region = Area of the whole fig. - area of the unshaded region

we have,

Solution:

$= (26 \times 12) - 4 \times (20 - 2 \times 2) + \pi {(2)}^{2} \\ = 312 - 4 \times (20 - 4) + \pi4 \\ = 312 - 4 \times 16 + \pi4 \\ = 312 - 64 + \pi4 \\ = 248 + \pi4 \\ = 260.56 \: {m}^{2} \: approx.$