A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid?
Accepted Solution
A:
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 = 5cmTherefore 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]