Question

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? ​

Answer 1

Answer:

The correct option is D) $\frac{2}{3}$

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 $l\times b$

Where, l = 6 cm + 3 cm = 9 cm and b = 5cm

Therefore the area of the rectangle is;

Area of rectangle = $9cm\times 5cm=45cm$

Now find the area of trapezoid.

The area of trapezoid is: $\frac{a+b}{2}h$

Where h is the height and a and b are the parallel sides.

Area of trapezoid = $\frac{9+3}{2}\times 5=30$

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:

$Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}$

$Probability=\frac{30}{45}=\frac{2}{3}$

Hence, the correct option is D) $\frac{2}{3}$