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Chapter 7: Problem 31

Find the perimeter of a regular pentagon that measures 3.5 in. on each side.

Short Answer

Expert verified
The perimeter of the pentagon is 17.5 inches

Step by step solution

01

Understanding the problem

The problem asks to find the perimeter of a regular pentagon. The perimeter of a regular polygon is calculated by multiplying the length of one side by the number of sides.
02

Identify the number of sides of a pentagon

A pentagon is a five-sided polygon. Therefore, the number of sides is 5.
03

Calculate the perimeter

Using the formula for the perimeter of a polygon, which is the length of one side multiplied by the number of sides, we get \(3.5 \, inches \times 5 = 17.5 \, inches\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Regular Pentagon
A regular pentagon is a polygon with five equal sides and five equal angles. When we say "regular," we mean that not only are all sides of the pentagon the same length, but all of its interior angles are also equal. Each angle in a regular pentagon is 108 degrees.

Regular pentagons are common in nature and design, such as in the shape of a home plate in baseball or the framework of certain flowers. Understanding these properties helps in identifying and working with shapes in various problems like calculating the perimeter.
Geometry
Geometry is a branch of mathematics that involves the study of shapes, sizes, and properties of space. It covers figures like lines, angles, shapes, and their relationships with one another.

Understanding geometry helps in visualizing objects and solving problems that involve measurements and calculations. For example:
  • Recognizing how shapes like pentagons fit into larger structures
  • Using the properties of regular polygons to solve real-world problems
  • Applying formulas, such as calculating perimeters and areas
Grasping basic geometry concepts is essential to progress in math and understand the world around us.
Polygon
A polygon is a closed, two-dimensional shape with straight sides. These sides are called edges, and the points where they meet are called vertices. The simplest polygon, a triangle, has three sides, while polygons can have many more sides, such as pentagons (five sides) or hexagons (six sides).

Polygons can be regular, where all sides and angles are equal, or irregular, with varying side lengths and angles. Recognizing different types of polygons is useful for identifying shapes in math problems and in everyday life.
Prealgebra
Prealgebra is a foundational math course that prepares students for the study of algebra. It covers basic arithmetic and the introduction of concepts that will be crucial in algebra and subsequent math courses.

Some key components of prealgebra include:
  • Understanding operations with whole numbers, fractions, and decimals
  • Grasping the concept of basic shapes and their properties, including polygons like regular pentagons
  • Simplifying expressions and solving simple equations
Through prealgebra, students develop strong computational skills and an understanding of basic mathematical properties.

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Most popular questions from this chapter

An oil storage tank, which is in the shape of a cylinder, is 4 m high and has a diameter of \(6 \mathrm{m}\). The oil tank is two-thirds full. Find the number of cubic meters of oil in the tank. Round to the nearest hundredth.

A circle has a radius of 8 in. Find the increase in area when the radius is increased by 2 in. Round to the nearest hundredth.

What is the area of a square patio that measures \(8.5 \mathrm{m}\) on each side?

The height of a parallelogram is \(3.4 \mathrm{m},\) and the length of the base is \(5.2 \mathrm{m}\). Find the arga of the parallelogram.

The diameter of the base of a cylinder is \(24 \mathrm{cm} .\) The height of the cylinder is \(18 \mathrm{cm} .\) Find the volume of the cylinder. Round to the nearest hundredth.
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