To find the area of a triangle, we can use the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] ### Step-by-Step Explanation 1. **Identify the Base and Height**: - In this problem, the base of the triangle is given as 10 cm, and the height is given as 6 cm. 2. **Substitute the Values into the Formula**: - We substitute the values of the base and height into the area formula: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} \] 3. **Perform the Multiplication**: - First, multiply the base and height: \[ 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2 \] 4. **Multiply by \(\frac{1}{2}\)**: - Now, take half of 60 cm²: \[ \text{Area} = \frac{1}{2} \times 60 \, \text{cm}^2 = 30 \, \text{cm}^2 \] 5. **Final Answer**: - Therefore, the area of the triangle is **30 cm²**. ### Why Option A is Correct - The calculations show that the area of the triangle is indeed 30 cm², which corresponds to option A. ### Explanation of Other Options - **Option B (40 cm²)**: This option is incorrect because it does not follow from the area formula. If we mistakenly multiplied the base and height without taking half, we would get 60 cm², but halving it correctly gives us 30 cm², not 40 cm². - **Option C (60 cm²)**: This option represents the product of the base and height without applying the \(\frac{1}{2}\) factor. While it is a common mistake to forget to divide by 2, the area of a triangle must always be half of the rectangle formed by the base and height. - **Option D (20 cm²)**: This option is also incorrect. It could arise from a misunderstanding of the formula or incorrect calculations. For example, if someone mistakenly used a base of 5 cm instead of 10 cm, they might arrive at 20 cm², but that does not apply here. ### Common Pitfalls - Forgetting to multiply by \(\frac{1}{2}\) is a frequent mistake when calculating the area of a triangle. - Confusing the area of a triangle with that of a rectangle, which does not require halving. - Misreading the values for base and height can lead to incorrect calculations. ### Revision Summary - The area of a triangle is calculated using the formula: \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\). - For a base of 10 cm and height of 6 cm, the area is 30 cm². - Always remember to divide the product of base and height by 2. - Double-check your values for base and height to avoid calculation errors.