Question

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Answer 1

Area of the figure:
Af = a² + 2 a²/4 π = 2.57 a²
Area of the shaded region:
As = 2 a²/4 π = 1.57 a²
x = (1.57 · 100) / 2.57 = 61 % ≈ 60 %
Answer: B) about 60 %

Answer 2

Answer:

B. about 60%

Step-by-step explanation:

Let us assume that the radius of the semi-circle is d units.

So the area of the semi-circle will be,

$=\dfrac{\pi d^2}{2}$

In total there are 4 semi circles, so the net area will be,

$=4\times \dfrac{\pi d^2}{2}$

$=2\pi d^2$

The side length of the square is twice the radius of the semi circle. So the side length of the square is 2d units.

Area of the square is,

$=(2d)^2\\\\=4d^2$

The total area will be,

$=2\pi d^2+4d^2$

So that the random point will be in the shaded region is,

$=\dfrac{\text{Area of semi circles}}{\text{Area of square}}$

$=\dfrac{2\pi d^2}{2\pi d^2+4d^2}$

$=\dfrac{2\pi}{2\pi+4}$

$=0.6$

$=60\%$