Answer:
[tex]p\approx 0.39[/tex]
Step-by-step explanation:
We are given a circle of radius 4 cm, and a triangle inscribed within the circle with a vertical height of 6.5 cm and a base of 6 cm.
To find the probability a randomly selected point lands in the red area, we can divide the red area by the total area.
The area for a circle is given by:
[tex]A=\pi r^2[/tex]
Since the radius is 4 cm, the area of the circle or total area is:
[tex]A=\pi (4)^2=16\pi \text{ cm}^2[/tex]
The area for a triangle is given by:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
The base of the triangle is 6 cm total and the vertical height is 6.5 cm. Therefore, the area is:
[tex]\displaystyle A=\frac{1}{2}(6)(6.5)=19.5\text{ cm}^2[/tex]
The probability of landing in the red shaded area is:
[tex]\displaystyle p=\frac{\text{Red Region}}{\text{Total Region}}[/tex]
Therefore:
[tex]\displaystyle p=\frac{19.5}{16\pi}\approx 0.39=39\%[/tex]
