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: \( \text{Area} = \text{length} \times \text{width} \). In this case, the length is 6 cm and the width is 5 cm. So, the area of the rectangle is \( 6 \text{ cm} \times 5 \text{ cm} = 30 \text{ cm}^2 \).

The area of a right triangle is given by the formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). In this case, the base is 3 cm and the height is 4 cm. So, the area of the triangle is \( \frac{1}{2} \times 3 \text{ cm} \times 4 \text{ cm} = 6 \text{ cm}^2 \).

The area of the shaded region is the area of the rectangle minus the area of the triangle. So, the area of the shaded region is \( 30 \text{ cm}^2 - 6 \text{ cm}^2 = 24 \text{ cm}^2 \).

Final Answer The final answer is $\boxed{24 \text{ cm}^2}$