Question

calculating geometric probability complete the steps to find the probability that a randomly chosen point on the triangle is in the shaded rectangle. the area of the triangle is □ cm². the area of the rectangle is □ cm². the probability that the point is in the shaded area is □.

Explanation:

Step1: Calculate area of triangle

The formula for the area of a right triangle is $\frac{1}{2} \times base \times height$. Here, base = 20 cm and height = 15 cm.
$$\text{Area of triangle} = \frac{1}{2} \times 20 \times 15 = 150 \text{ cm}^2$$

Step2: Calculate area of rectangle

The formula for the area of a rectangle is $length \times width$. Here, length = 8 cm and width = 6 cm.
$$\text{Area of rectangle} = 8 \times 6 = 48 \text{ cm}^2$$

Step3: Calculate probability

Probability is the ratio of the area of the rectangle (shaded region) to the area of the triangle.
$$\text{Probability} = \frac{\text{Area of rectangle}}{\text{Area of triangle}} = \frac{48}{150} = \frac{8}{25} = 0.32$$

Answer:

• The area of the triangle is $\boldsymbol{150}$ $\text{cm}^2$.
• The area of the rectangle is $\boldsymbol{48}$ $\text{cm}^2$.
• The probability that the point is in the shaded area is $\boldsymbol{\frac{8}{25}}$ (or 0.32).