Math Problem Statement
Solution
The problem in the image is asking to find the lateral surface area of a right prism, where the base is a right triangle with legs measuring 3 cm and 4 cm, and the height of the prism is 4 cm. Let's break down the steps to solve it.
Steps:
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Determine the Perimeter of the Base: The base is a right triangle with legs 3 cm and 4 cm. The hypotenuse can be found using the Pythagorean theorem:
The perimeter of the triangular base is the sum of all its sides:
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Calculate the Lateral Surface Area: The lateral surface area of a prism is given by the formula:
where is the perimeter of the base and is the height of the prism. Given that the height of the prism is 4 cm:
Final Answer:
The lateral surface area of the prism is , which corresponds to option Д.
Would you like a more detailed explanation, or do you have any questions?
Here are five related questions to expand on this concept:
- How would the lateral surface area change if the height of the prism were doubled?
- What would be the total surface area of the prism, including the bases?
- How do you find the volume of this prism?
- What is the lateral surface area of a cylinder with the same height and perimeter as this prism?
- How would the lateral surface area change if the triangle's legs were halved?
Tip: In right prisms, the lateral surface area is always found by multiplying the perimeter of the base by the height of the prism.
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area of Prisms
Right Triangles
Formulas
Pythagorean theorem: c = √(a^2 + b^2)
Lateral surface area of prism: A_lateral = P × h
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 8-10
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