NUMBER 5:
INFORMATION:
We have a trapeze and, we need to find the probability that a randomly chosen point is the figure lies in the shaded region
STEP BY STEP EXPLANATION:
To find the probability, we must divide the area of the shaded region by the total area of the trapeze
[tex]\text{ Probability}=\frac{Shaded\text{ area}}{Total\text{ area}}[/tex]- Total area:
To calculate the total area, we must use the formula for the area of a trapeze
[tex]A_{trapeze}=\frac{(b_1+b_2)h}{2}[/tex]Where, b1 and b2 are the bases and h is the height
Then, analyzing the trapeze we can see that b1 = 20, b2 = 14 and h = 12
[tex]A_{total}=A_{trapeze}=\frac{(20+14)12}{2}=204[/tex]So, the total area is 204 square units
- Shaded area:
To find the shaded area, we must subtract the no shaded area from the total area.
We can see that the no shaded area is a rectangle with width = 14 and height = 12
Now, using the formula for the area of a rectangle
[tex]A_{rectangle}=\text{ width}\times\text{ height}=14\times12=168[/tex]Then, subtracting the area of the rectangle from the total area
[tex]A_{\text{ no shaded}}=204-168=36[/tex]So, the no shaded are is 36 square units.
Finally, the probability would be
[tex]\begin{gathered} \text{ Probability}=\frac{36}{204} \\ \text{ Simplifying,} \\ \frac{3}{17}\approx17.65\text{ \%} \end{gathered}[/tex]ANSWER:
the probability that a randomly chosen point is the figure lies in the shaded region is
[tex]\frac{3}{17}\approx17.65\text{ \%}[/tex]