Math Problem Statement
Solution
The problem is asking for the lateral surface area of a triangular pyramid, given the base is an equilateral triangle, and the faces are congruent.
To find the lateral surface area, we need to calculate the area of the three congruent triangular faces. Here's how to approach it:
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Base of the Triangle: The base of the equilateral triangle is given as 4 meters.
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Height of each triangular face: The slant height of the pyramid, which is 5.2 meters, will be used to calculate the area of each triangular face.
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Area of one triangular face: The area of each congruent triangular face can be calculated using the formula for the area of a triangle:
The base is 4 m (side of the equilateral triangle), and the height of each face is 5.2 m (the slant height). -
Total lateral surface area: Since there are three congruent faces, multiply the area of one face by 3:
Thus, the lateral surface area of the triangular pyramid is 31.2 square meters.
Would you like more details on how to approach the problem or any clarification? Here are a few related questions you could explore next:
- How do you calculate the surface area of a pyramid with a square base?
- What is the difference between slant height and vertical height in a pyramid?
- How would the lateral surface area change if the height of the triangular faces was different?
- What is the formula for the volume of a pyramid, and how does it relate to the surface area?
- How would you calculate the total surface area of a pyramid?
Tip: Always make sure to differentiate between slant height and vertical height when calculating the surface area of pyramids!
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area
Triangular Pyramid
Formulas
Area of one triangular face = 1/2 × base × height
Lateral Surface Area = 3 × Area of one triangular face
Theorems
Area of triangle
Properties of equilateral triangles
Suitable Grade Level
Grades 7-9
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