Math Problem Statement

What is the lateral surface area, in square meters, of the triangular pyramid?

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:

  1. Base of the Triangle: The base of the equilateral triangle is given as 4 meters.

  2. 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.

  3. Area of one triangular face: The area of each congruent triangular face can be calculated using the formula for the area of a triangle:
    Area of one face=12×base×height of the face\text{Area of one face} = \frac{1}{2} \times \text{base} \times \text{height of the face} The base is 4 m (side of the equilateral triangle), and the height of each face is 5.2 m (the slant height).

    Area of one face=12×4m×5.2m=10.4m2\text{Area of one face} = \frac{1}{2} \times 4 \, \text{m} \times 5.2 \, \text{m} = 10.4 \, \text{m}^2

  4. Total lateral surface area: Since there are three congruent faces, multiply the area of one face by 3: Lateral surface area=3×10.4m2=31.2m2\text{Lateral surface area} = 3 \times 10.4 \, \text{m}^2 = 31.2 \, \text{m}^2

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:

  1. How do you calculate the surface area of a pyramid with a square base?
  2. What is the difference between slant height and vertical height in a pyramid?
  3. How would the lateral surface area change if the height of the triangular faces was different?
  4. What is the formula for the volume of a pyramid, and how does it relate to the surface area?
  5. 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