In given figure, four semicircles have been drawn within the given square whose side is 2 units. The centres of these semicircles are the midpoints of the sides. They create a 4-petalled flower (shown in gray). Find the perimeter and the area of this flower.

Each side of the square is 2, so every semicircle has radius $r = 1$.

Each blue petal is formed by the intersection of two quarter-circles of radius 1.

Perimeter of flower:

One petal boundary consists of two arcs.

Each arc is a quarter-circle of radius 1.

Length of one quarter-circle arc:

$$\frac{1}{4}(2\pi r) = \frac{\pi}{2}$$

So, perimeter of one petal: $2\left(\frac{\pi}{2}\right) = \pi$

There are 4 petals.

Hence, total perimeter = $4\pi$.

Area of flower:

Consider one petal.

It is made from two 90° sectors minus a square-like kite in between.

Area of one 90° sector:

$$A = \frac{\theta}{360^\circ} \pi r^2$$

With $\theta = 90^\circ$ and $r = 1$, sector area = $\frac{1}{4}\pi$

Two such sectors give: $\frac{\pi}{2}$

Inside them is a right triangle with legs 1 and 1.

Triangle area: $A = \frac{1}{2}bh$

$$\frac{1}{2}(1)(1) = \frac{1}{2}$$

So, area of one petal is $\frac{\pi}{2} - 1$.

For area of whole flower:

There are 4 identical petals.

$$\text{So, } 4\left(\frac{\pi}{2} - 1\right) = 2\pi - 4$$

Therefore, Area = $2\pi - 4$ square units.