Triangular Pyramid

Properties of a Triangular Pyramid:

• It has 4 faces: 1 triangular base and 3 triangular lateral faces.
• It has 6 edges.
• It has 4 vertices.
• The altitude of the pyramid is the perpendicular distance from the apex to the base.
• The slant height of the pyramid is the distance from the apex to the midpoint of an edge of the base.

Formulas for Triangular Pyramid:

The surface area (A) of a triangular pyramid can be calculated using the formula:

A = 0.5 * base perimeter * slant height + base area

The volume (V) of a triangular pyramid can be calculated using the formula:

V = (1/3) * base area * height

Example Problem:

Find the surface area and volume of a triangular pyramid with a base side length of 5 cm, base height of 4 cm, and slant height of 7 cm.

Base Area = (1/2) * base side length * base height = (1/2) * 5 cm * 4 cm = 10 cm²

Surface Area = 0.5 * (3 * 5 cm) * 7 cm + 10 cm² = 52.5 cm²

Volume = (1/3) * 10 cm² * 4 cm = 13.33 cm³

Study Guide:

When studying triangular pyramids, focus on understanding the relationship between the base, height, slant height, and apex. Practice using the surface area and volume formulas and solving problems involving triangular pyramids. It's also important to be familiar with the properties and characteristics of triangular pyramids, such as the number of faces, edges, and vertices.

Remember to visualize the shape of a triangular pyramid in 3D space to better understand its properties and how to calculate its surface area and volume.