Find the area of the shaded region in the given figure where PQRS is a square of side and A, B, C, D are the midpoints of PQ, QR, RS and PS.

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30.96

42.54

28 ${"mathml":"<math class="image_resized" style="width:25px;height:13px"><span style="font-family:$

answer is A.

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Detailed Solution

Concept- The figure makes it obvious that PQRS is a square with a side of 12 cm and is engraved with four quarter circles.Therefore, we must compute a square's size and deduct a four-quarter circle's area from it.
Using 12 cm for the square's side
First, determine the square's area, which is equal to 2a, where an is its side length.
${"mathml":"<math class="image_resized" style="width:189px;height:16px"><span style="font-family:$ Now, let's examine any one of the quarter circles as they are all comparable. For example, if we look at DSC, we can see that its radius is DS, which is equal to half the length of a square's side.
So , r = 122 = 6 cm
Therefore, a quarter circle's area is
{"mathml":"<math class=

Consequently, the total area of the four quarter circles is
${"mathml":"<math class="image_resized" style="width:88px;height:64px"><span style="font-family:$ Consequently, the darkened portion's area is
${"mathml":"<math class="image_resized" style="width:100px;height:65px"><span style="font-family:$ Hence, the correct option is 1) 30.96 ${"mathml":"<math class="image_resized" style="width:25px;height:13px"><span style="font-family:$

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