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