Question

What is the perimeter of a sheet of paper that is \(25.2 \mathrm{~cm}\) tall and \(18.1 \mathrm{~cm}\) wide?

Short answer

The perimeter is 86.6 cm.

Step-by-step solution

Understand the Shape

A sheet of paper is generally rectangular in shape. Each rectangle has two pairs of opposite sides that are equal. We are given one pair of sides as the height, which is 25.2 cm, and another pair as the width, which is 18.1 cm.

Recall the Perimeter Formula

The perimeter of a rectangle is given by the formula: \[ P = 2(l + w) \]where \( l \) is the length (or height in this case) and \( w \) is the width of the rectangle.

Substitute Known Values

Substitute the height for \( l \) and the width for \( w \) in the formula:\[ P = 2(25.2 + 18.1) \]

Calculate the Sum Inside the Parenthesis

Calculate the sum of the height and the width inside the parenthesis:\[ 25.2 + 18.1 = 43.3 \]

Calculate the Perimeter

Now, multiply the sum by 2 to find the perimeter:\[ P = 2 imes 43.3 = 86.6 \]

State the Final Answer

The perimeter of the sheet of paper is 86.6 cm.

Key concepts

Understanding Geometry of Perimeter

Geometry is a branch of mathematics that deals with shapes, sizes, and the properties of space. It's all around us, from the layout of a room to the shape of a pizza! With geometry, we can measure and understand the world better. The concept of perimeter is part of geometry. It deals with the total length around a shape.

The perimeter can be thought of as a fence you might build around your yard. For a rectangle, the perimeter is the sum of all the side lengths enclosing the space. When you know the measurements of the sides, calculating the perimeter becomes a straightforward task.

Whether you are studying a triangle, circle, or rectangle, understanding how to calculate the perimeter is essential for solving real-world problems. In our problem, we focused on a rectangular shape—just like a sheet of paper!

The Structure of a Rectangle

A rectangle is a simple shape that we encounter every day. It's defined as a quadrilateral where opposite sides are equal and it has four right angles. This makes it easy to find the perimeter if you know the length and width.

Key features of a rectangle include:

• Four sides
• Opposite sides are equal
• Four right angles

For example, if you have a piece of paper, it's typically a rectangle. Here, the longer side is usually referred to as the length (or height), and the shorter side is the width.

Understanding these basic characteristics helps simplify the process of measuring the perimeter and solving related mathematical problems. In our original exercise, the dimensions given, 25.2 cm and 18.1 cm, directly informed our perimeter calculation.

Mathematics Problem Solving: Finding the Perimeter

Math problem solving often involves breaking a question into smaller, more manageable parts. In the given exercise, we dealt with finding the perimeter of a rectangle.

We follow a structured approach:

• Identify what is being asked: Here it's the perimeter of a rectangle.
• Recall or find the relevant formula: For a rectangle, it's \( P = 2(l + w) \).
• Substitute the known values into the formula: Use the given dimensions.
• Perform the operations as per the formula instructions.
• Double-check your calculations for accuracy.

In practice, \( P = 2(l + w) \) means you will add the length and width together and then double the total, capturing all the side lengths of the rectangle.

Consistent practice with these methods helps develop efficient problem-solving skills in mathematics, ensuring that errors are minimized and solutions are clear and logical.