Problem 14 - Basic Technical Mathematics with Calculus

Question

Find the area of each figure. Square: \(\quad s=15.6 \mathrm{ft}\)

Step-by-Step Solution

Answer

The area of the square is 243.36 square feet.

Step 1: Understand the Problem

We are asked to find the area of a square with a side length of 15.6 feet. In geometry, the area of a square is calculated using the side length.

Step 2: Recall the Formula for Area of a Square

The area of a square can be determined using the formula: \[A = s^2\]where \(s\) is the length of one side of the square.

Step 3: Substitute the Value

Substitute the given side length \(s = 15.6\) feet into the formula:\[A = (15.6)^2\]

Step 4: Calculate the Area

Perform the calculation:\[A = 15.6 imes 15.6 = 243.36 ext{ square feet}\]

Step 5: State the Final Answer

The area of the square is 243.36 square feet.

Key Concepts

Geometry Formulas

Geometry is full of fascinating formulas designed to help us understand the shapes all around us. One of the most straightforward is the formula to find the area of a square. In general, the area of a geometric figure is the measure of the space inside it. Each shape has a specific formula that applies based on its properties and dimensions. For a square, which is a regular quadrilateral (meaning all sides are equal, and all angles are right angles), the area formula is simple and elegant. This formula, \(A = s^2\), depends solely on the side length (s) of the square.

• The beauty of geometry formulas lies in their simplicity and reliability.
• Understanding these formulas can demystify the process of area calculation.

In learning geometry, getting comfortable with these formulas is key to unlocking the potential of mathematical problem solving.

Square Area Calculation

Calculating the area of a square is one of the most fundamental skills in geometry. When you know the length of one side, the process becomes almost automatic due to the simplicity of the formula. First, recognize that a square's sides are all equal in length, which means you only need one measurement to find its area. The formula for the area of a square is: \[A = s^2\]\Here's how it works step-by-step:

• Find the side length (\(s\)) of the square. For example, suppose \(s = 15.6 \, \text{ft}\).
• Substitute this measurement into the formula: \[A = (15.6)^2\]
• Multiply the side length by itself: \[A = 15.6 \times 15.6 = 243.36\]

By using this simple approach, you can quickly and accurately determine that the area of this square is 243.36 square feet.

Mathematical Problem Solving

Problem solving in mathematics often involves a series of logical steps that lead to the solution. In solving for the area of a square, the approach is systematic and requires:

• Understanding the problem: Knowing what is given and what needs to be found.
• Recalling relevant formulas: Applying the right formula, knowing \(A = s^2\) for a square.
• Substituting values: Plugging in the known side length into the formula.
• Performing calculations: Executing the math to find your answer, using honest arithmetic.

This process serves as a framework for tackling more complex mathematical problems. Each step builds upon the other to ensure that no detail is overlooked, and the solution is sound. Encouraging this problem-solving mindset helps develop mathematical intuition and proficiency in handling various kinds of tasks. Always verify your answer to ensure accuracy and build confidence in your mathematical skills.