Here's a well-structured article that explains the formula and calculation of the surface area of an isosceles triangular prism:

Triangular Prism Surface Area Formula Examples

When it comes to calculating the surface area of three-dimensional shapes, understanding the concept of lateral area and surface area is crucial. In this article, we will explore the formula for finding the surface area of an isosceles triangular prism, along with some examples.

What is Lateral Area?

Lateral area refers to the total area of the lateral or vertical faces of any solid. In the case of an isosceles triangular prism, the lateral area is found by summing up the areas of all the vertical faces.

Derivation of Surface Area of Isosceles Triangular Prism

To find the surface area of an isosceles triangular prism, we need to break it down into its individual components. Since the vertical faces in this case are rectangles, we can calculate their areas separately and then add them up.

The formula for finding the lateral area of an isosceles triangular prism is:

LA = Sum of the areas of all the vertical faces

= Sum of the areas of the three rectangles

To find the surface area (SA), we need to add the area of the two isosceles triangles at the base facing each other and the area of the rectangles formed by the corresponding sides of the two congruent triangles.

SA = Sum of areas of 2 isosceles triangles + Sum of the areas of the 3 rectangles

Formula for Surface Area of Isosceles Triangular Prism

The formula for finding the surface area of an isosceles triangular prism can be written as:

SA = Sum of areas of all the faces

This formula takes into account the areas of both the lateral and the base faces, providing a comprehensive calculation of the surface area.

Examples of Surface Area Calculation

To illustrate this concept further, let's consider some examples. Suppose we have an isosceles triangular prism with a base length of 5 cm and height of 4 cm. The corresponding sides of the two congruent triangles are 3 cm each. How do we calculate its surface area?

Using the formula provided earlier:

SA = Sum of areas of all the faces

= Area of 2 isosceles triangles + Area of the 3 rectangles

First, let's find the area of the two isosceles triangles.

Area of each triangle = (base × height) / 2

= (5 cm × 4 cm) / 2

= 10 cm²

Now, add the areas of both triangles:

Total area of triangles = 2 × 10 cm²

= 20 cm²

Next, find the area of each rectangle.

Area of each rectangle = base × height

= 3 cm × 4 cm

= 12 cm²

Now, add the areas of all three rectangles:

Total area of rectangles = 3 × 12 cm²

= 36 cm²

Finally, calculate the surface area by adding the total area of triangles and rectangles.

SA = Total area of triangles + Total area of rectangles

= 20 cm² + 36 cm²

= 56 cm²

Therefore, the surface area of our isosceles triangular prism is 56 cm². By applying this formula and calculation technique to various shapes, you can master the art of finding the surface area of complex three-dimensional objects.

In conclusion, calculating the surface area of an isosceles triangular prism requires a thorough understanding of lateral area and the concept of summing up individual face areas. With the formula SA = Sum of areas of all the faces, you can accurately determine the total area of this shape. By applying these concepts to real-world problems, you will become proficient in calculating the surface area of various three-dimensional shapes.

Triangular prism surface area formula examples