Final answer:
The height of the triangular prism is found by dividing the lateral area (300cm²) by the perimeter of the base (15cm), resulting in a height of 20 cm.
Step-by-step explanation:
The student asked what the height of a triangular prism is given that the base edges are 4cm, 5cm, and 6cm, and the lateral area is 300cm². To find the height, we can use the formula for the lateral surface area of a triangular prism: lateral area = perimeter of base × height. First, calculate the perimeter of the base, which is the sum of its sides:
- Perimeter = 4cm + 5cm + 6cm = 15cm
Then, using the given lateral area, we can find the height by rearranging the formula:
Height = Lateral Area / Perimeter
Height = 300cm² / 15cm = 20cm
Therefore, the height of the triangular prism is 20cm.