Math Example--Area and Perimeter--Surface Area: Example 7

Topic

Surface Area

Description

This example demonstrates the calculation of surface area for a hollow triangular prism with an equilateral triangular base. The outer triangle has a base of 10 units and a height of 5 * √(3), while the inner triangle has a base of 8 units and a height of 4 * √(3). The length of the prism is 35 units. The surface area is calculated by subtracting the area of the hollow region from the full prism's surface area, resulting in SA = b1 * h1 - b2 * h2 + 3 * l * w = (18 * √(3)) + 1050 square units.

Understanding surface area calculations for complex shapes like hollow prisms is essential in advanced mathematics and its applications. This collection of examples helps teach the topic by presenting progressively challenging scenarios, allowing students to apply and extend their knowledge of basic surface area principles to more sophisticated problems.

Engaging with multiple worked-out examples is crucial for students to fully comprehend advanced surface area calculations. Each example builds upon previous concepts while introducing new complexities, helping students develop critical thinking skills and the ability to approach novel geometric problems with confidence.

Teacher's Script: Today, we're tackling a more complex surface area problem involving a hollow triangular prism. Pay attention to how we adapt our previous knowledge to this new scenario. We'll calculate the surface area of the outer prism, then subtract the area of the hollow region. This approach will be useful when you encounter similar problems in real-world applications, such as in engineering or architecture.

 For a complete collection of math examples related to Surface Area click on this link: Math Examples: Surface Area Collection.