Problem 6 - Basic Technical Mathematics with Calculus

Question

Find the perimeter of each figure. Rhombus: side of \(2.46 \mathrm{ft}\)

Step-by-Step Solution

Answer

The perimeter of the rhombus is 9.84 ft.

Step 1: Recall the Perimeter Formula for a Rhombus

The perimeter of a rhombus is calculated by adding the lengths of all its sides. Since a rhombus has four equal sides, we can use the formula \( P = 4 imes s \), where \( s \) is the length of one side.

Step 2: Insert the Given Side Length

Substitute the given side length of the rhombus into the formula. Here, the side length \( s = 2.46 \) ft. Thus, the formula becomes \( P = 4 imes 2.46 \).

Step 3: Perform the Multiplication

Calculate the product of 4 and 2.46 to find the perimeter: \( P = 4 imes 2.46 = 9.84 \) ft.

Key Concepts

Rhombus

A rhombus is a unique type of quadrilateral, which is a four-sided polygon. It features some distinct characteristics that set it apart from other quadrilaterals. One of the main attributes of a rhombus is that all four of its sides are of equal length. This makes it similar to a square but with one key difference: the angles between the sides of a rhombus don't have to be 90 degrees. Instead, the opposite angles of a rhombus are equal.
Additionally, a rhombus can be visualized as a slanted square or a diamond shape, often related to geometric design patterns or artistic motifs. By understanding these fundamental properties, it becomes easier to grasp geometric concepts related to rhombuses, such as calculating their perimeter.

Geometry Formula

To solve geometric problems, especially in finding measures like the perimeter or area, using geometry formulas is crucial. The formula for calculating the perimeter of a rhombus is quite straightforward. Since a rhombus has four sides of equal length, the perimeter can be calculated by multiplying the length of one side by four. This formula can be expressed as:

• \( P = 4 \times s \)

where \( P \) is the perimeter, and \( s \) is the side length. This formula simplifies the process as you only need one given length. Such formulas, derived from fundamental geometric principles, empower students to efficiently tackle a range of tasks involving shapes with ease.

Step-by-Step Solution

Solving geometric problems step by step can make complex tasks more manageable. Consider the problem of finding the perimeter of a rhombus. Here's how you would approach it using a step-by-step method:

• **Recall the Formula**: Start by remembering or finding the perimeter formula. For a rhombus, it's \( P = 4 \times s \).
• **Insert the Given Values**: Plug in the known value, which is the side length of the rhombus. In our example, \( s = 2.46 \text{ ft} \).
• **Perform the Calculation**: Multiply the side length by 4 to find the perimeter. Calculate \( 4 \times 2.46 \). The perimeter is found to be \( 9.84 \text{ ft} \).

By following these steps, students can systematically address geometric problems and build confidence in solving them independently. These stages of understanding not only apply to rhombuses but also provide a framework for solving a wide array of geometric tasks.