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A triangular prism has base cdges 4cm,5cm, and 6cm long. Its lateral area is 300cm^(2). What is the height of the prism?

User Jigs
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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.

User Raja Ramesh
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