Problem 64 - Algebra 1: Concepts and Skills

Question

Find the area of the object. The cover of a children’s book is 4 inches long and 4 inches wide.

Step-by-Step Solution

Answer

The area of the book cover is 16 square inches.

Step 1: Understand the dimensions of the book cover

The book cover is a square with both length and width given as 4 inches.

Step 2: Use the formula to find the area of a square

The formula to find the area of a square is length times width. So, the area of the book cover is \(4 inches \times 4 inches = 16 square inches\).

Key Concepts

Finding Area

When we talk about finding the area of a shape, we refer to the amount of space that is enclosed within its boundaries. For flat, two-dimensional shapes, this is measured in square units. In our example, we are dealing with a square, which is one of the simplest shapes to work with as it has equal sides.

To calculate the area of a square, we multiply the length of one side by itself. This is because the definition of a square ensures that all sides are of equal length. In the case of the children's book cover from our exercise, with each side being 4 inches, the area calculation is straightforward: just multiply 4 inches by 4 inches to get 16 square inches. Recognizing that units also multiply, we end up with square inches as a measurement of area.

Square Dimensions

Understanding square dimensions is integral in geometry. A square is a special type of rectangle where all four sides are of the same length, which simplifies many calculations. The dimensions give us the length of the sides, and the properties of a square tell us that the angles between these sides are all right angles.

If you are given the length of one side of a square, you automatically know the lengths of all the other sides. This symmetry makes it very simple to compute the area, as you only need to know one dimension. With our 4-inch by 4-inch book cover, knowing that one side is 4 inches is enough, as all sides in a square are equal, and thus, we can use this one dimension to compute the area.

Math Problem Solving

Math problem solving involves a step-by-step approach to understanding and solving a given problem. The first step is comprehending the problem, which in our exercise involved recognizing the shape as a square and its equal dimensions.

Subsequently, applying the correct formula, which for a square is length multiplied by width, provides the solution. To become proficient in math problem solving, students should become familiar with different shapes and their properties, understand units of measurement, and know the relevant formulas. In addition, checking the result for reasonableness is key. For instance, if you calculated the area of our children's book to be 160 square inches, a sense of scale would tell you that such a large number for a small book cover is likely incorrect.