Answer:
The correct option is D) [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Consider the provided figure.
We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.
For this first find the total area as shown:
The given figure is a rectangle.
The area of rectangle is [tex]l\times b[/tex]
Where, l = 6 cm + 3 cm = 9 cm and b = 5cm
Therefore the area of the rectangle is;
Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]
Now find the area of trapezoid.
The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]
Where h is the height and a and b are the parallel sides.
Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]
Thus, the area of trapezoid is 30 cm.
Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:
[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]
[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]
Hence, the correct option is D) [tex]\frac{2}{3}[/tex]
