Answer:
30%
Explanation:
To solve this, you must first find the areas of the circle and the pentagon within it.
Find the area of the circle:
The area of a circle is πr² and the circle in the diagram is shown to have a radius of 4cm, so to find its area, plug 4 into the equation
A = πr² ⇒ A = π(4)² ⇒ A = 16π
Find the area of the pentagon:
To find the area of a pentagon, you should first know that the shape is simply five triangles combined into one shape. (See Image)
With the formula for the area of a triangle in mind, it should be known that the pentagon's side acts as a base and the pentagon's apothem (dotted line) acts as a height for each triangle. According to the diagram, the base length is 4.7 and the height is 3.2. To find the area of any of the triangles, plug these values into the formula for the area of a triangle:
A =
bh ⇒ A =
(4.7)(3.2) ⇒ A = 7.52 cm²
Since a pentagon is made of five of these, simply multiply the area you just found by 5 to find its area:
A = 7.52 * 5 = 37.6 cm²
Find the area of the white parts:
To find the area of the white parts, subtract the area of the pentagon from the area of the circle:
16π - 37.6 = 12.67 cm²
Now all that's left is to find the probability, all you have to do is
Divide the area of the white by the area of the circle:
12.67 / 16π = .25, which is .3 rounded to the nearest tenth.
That means that the probability that a randomly selected point within the circle falls in the white area is 30%
Hope this worked!