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 5 cm. 2. **Substitute the Values into the Formula**: - We substitute the values of the base and height into the area formula: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 5 \, \text{cm} \] 3. **Perform the Multiplication**: - First, multiply the base and height: \[ 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2 \] 4. **Multiply by \(\frac{1}{2}\)**: - Now, take half of the result: \[ \text{Area} = \frac{1}{2} \times 50 \, \text{cm}^2 = 25 \, \text{cm}^2 \] 5. **Final Result**: - Therefore, the area of the triangle is **25 cm²**. ### Conclusion The correct option is **B. 25 cm²**. ### Explanation of Other Options - **Option A: 15 cm²**: This option is incorrect because it does not follow the area formula. It seems to be a random number that does not relate to the calculations we performed. - **Option C: 50 cm²**: This option represents the product of the base and height without dividing by 2. While it is the area of a rectangle with the same base and height, it does not account for the fact that a triangle only occupies half that area. - **Option D: 100 cm²**: This option is also incorrect as it suggests an area that is four times larger than the actual area. It may arise from a misunderstanding of the area formula or a miscalculation. ### Common Pitfalls - **Forgetting to Divide by 2**: A common mistake is to forget that the area of a triangle is half the product of the base and height. - **Confusing Triangle with Rectangle**: Some students might mistakenly use the rectangle area formula (base × height) instead of the triangle formula. ### 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 5 cm, the area is 25 cm². - Always remember to divide by 2 when calculating the area of a triangle. - Be cautious of confusing the area of a triangle with that of a rectangle.