Triangular Prism

A triangular prism is a three-dimensional shape that has two parallel triangular bases and three rectangular faces. The two triangular bases are connected by three rectangular faces, creating a prism with a triangular cross-section.

Characteristics of a Triangular Prism

1. Bases: The triangular prism has two parallel triangular bases. These bases are identical in shape and size.

2. Faces: A triangular prism has 5 faces - 2 triangular bases and 3 rectangular faces.

3. Edges: It has 9 edges - 3 from each triangular base and 3 connecting the rectangular faces.

4. Vertices: A triangular prism has 6 vertices - 3 on each triangular base.

Formulas for a Triangular Prism

Surface Area: The surface area (SA) of a triangular prism can be calculated using the formula:

SA = 2 * base area of the triangle + perimeter of the triangle * height of the prism

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

V = base area of the triangle * height of the prism

Example Problem

Find the surface area and volume of a triangular prism with the following dimensions:

Base of the triangle = 5 cm

Height of the triangle = 8 cm

Height of the prism = 12 cm

Solution:

Base area of the triangle = (1/2) * base * height = (1/2) * 5 * 8 = 20 cm²

Perimeter of the triangle = 3 * base = 3 * 5 = 15 cm

Surface Area (SA) = 2 * 20 + 15 * 12 = 40 + 180 = 220 cm²

Volume (V) = 20 * 12 = 240 cm³

Study Guide

When working with triangular prisms, it's important to understand the following concepts:

Identifying the bases, faces, edges, and vertices of a triangular prism
Using the formulas for calculating the surface area and volume of a triangular prism
Applying the concepts to solve real-world problems involving triangular prisms

Practice calculating the surface area and volume of different triangular prisms with varying dimensions to strengthen your understanding of the topic.

Remember to pay attention to the units of measurement and apply the correct formula based on the given information to arrive at the accurate solutions.

By mastering the concepts and formulas related to triangular prisms, you'll be well-prepared to handle problems involving these three-dimensional shapes with confidence.

◂Math Worksheets and Study Guides Seventh Grade. Rational and Irrational Numbers

Study Guide

Rational and Irrational Numbers

Worksheet/Answer key

Rational and Irrational Numbers

Worksheet/Answer key

Rational and Irrational Numbers

Worksheet/Answer key

Rational and Irrational Numbers

The resources above cover the following skills:

Connections to the Grade 7 Focal Points (NCTM)

Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.