Questions: A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

Solution Steps

The area of a rectangle is given by the formula: \[ \text{Area} = \text{length} \times \text{width} \] For the given rectangle: \[ \text{length} = 9 \, \text{cm} \] \[ \text{width} = 6 \, \text{cm} \] \[ \text{Area of the rectangle} = 9 \, \text{cm} \times 6 \, \text{cm} = 54 \, \text{cm}^2 \]

The area of a right triangle is given by the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For the given right triangle: \[ \text{base} = 6 \, \text{cm} \] \[ \text{height} = 3 \, \text{cm} \] \[ \text{Area of the right triangle} = \frac{1}{2} \times 6 \, \text{cm} \times 3 \, \text{cm} = 9 \, \text{cm}^2 \]

To find the area of the shaded region, subtract the area of the right triangle from the area of the rectangle: \[ \text{Area of the shaded region} = \text{Area of the rectangle} - \text{Area of the right triangle} \] \[ \text{Area of the shaded region} = 54 \, \text{cm}^2 - 9 \, \text{cm}^2 = 45 \, \text{cm}^2 \]

Final Answer