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

2/3

Explanation:

I got it right

Answer 2

The correct option is D)
`(2)/(3)`

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* b`

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

Therefore the area of the rectangle is;

Area of rectangle =
`9cm* 5cm=45cm`

Now find the area of trapezoid.

The area of trapezoid is:
`(a+b)/(2)h`

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

Area of trapezoid =
`(9+3)/(2)* 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=(30)/(45)=(2)/(3)`

Hence, the correct option is D)
`(2)/(3)`