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Chapter 7: Problem 71

The length of a side of a square is \(12.5 \mathrm{cm} .\) Find the area of the square.

Short Answer

Expert verified
The area of the square is 156.25 square cm.

Step by step solution

01

Understand the formula for the area of a square

The area of a square is calculated by squaring the length of one side. The formula is \(Area = side^2\).
02

Substitute the Given Value

Substitute the value of the side (given as 12.5cm) into the formula. So, \(Area = (12.5 \, cm)^2\).
03

Calculation

Calculate the area by raising 12.5 cm to the power of 2. This equals 156.25 square cm.

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Key Concepts

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

Area of a Square
The area of a square is an essential concept in geometry. It measures the amount of space inside a square. To find this area, you simply multiply the length of one side by itself. This is because a square has four equal sides, and its shape involves symmetry.
The formula for calculating the area of a square is:
  • Area = side \( \times \) side
  • Alternatively written as \( \text{Area} = \text{side}^2 \)
In the given problem, the side of the square is \(12.5 \, \text{cm}\). By using the formula, we find the area is \((12.5 \, \text{cm})^2\), which simplifies to \(156.25 \, \text{square cm}\). Calculating the area helps in understanding how much surface the square covers.
Understanding Formulas
Understanding mathematical formulas is crucial for solving geometry problems efficiently. A formula is a rule that shows how variables are connected, helping you quickly calculate desired values.
For instance, the formula for the area of a square is \( \text{Area} = \text{side}^2 \). This formula tells us that to calculate the area, we raise the length of the square's side to the power of two.
  • It's important to identify key components in a formula, like what each variable represents.
  • Substitute given values correctly into the formula to get accurate results.
The practice of using formulas simplifies calculations and helps solve complex problems by applying a consistent procedure. Start by breaking down the formula into understandable parts and practice substituting values.
Calculations with Exponents
Exponents play a vital role in many mathematical calculations, including finding the area of a square. An exponent tells you how many times to multiply a number by itself.
In the formula \( \text{Area} = \text{side}^2 \), the exponent "2" indicates the side of the square is multiplied by itself. This is also known as "squaring" a number.
  • For example, \(12.5^2\) means \(12.5 \times 12.5\).
  • Raising a number to the power of 2 is common when finding areas.
Understanding how exponents work allows you to perform calculations more accurately and efficiently. Always take care to perform the multiplication correctly, especially when working with decimals or larger numbers. Practice calculating with exponents to become more comfortable with these types of problems.

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Most popular questions from this chapter

Determine whether the statement is always true, sometimes true, or never true. a. The slant height of a regular pyramid is longer than the height. b. The slant height of a cone is shorter than the height. c. The four triangular faces of a regular pyramid are equilateral triangles.

Find the ratio of the areas of two squares if the ratio of the lengths of their sides is 2: 3.

A can of paint will cover \(300 \mathrm{ft}^{2}\). How many cans of paint should be purchased in order to paint a cylinder that has a height of \(30 \mathrm{ft}\) and a radius of \(12 \mathrm{ft} ?\)

A 30 -foot ladder leans against the side of a building with its bottom \(a\) feet from the building. The ladder reaches a height of \(b\) feet on the building. Which of the following distances is not possible as a value for \(b ?\) (i) \(5 \mathrm{ft}\) (ii) \(25 \mathrm{ft}\) (iii) \(35 \mathrm{ft}\)

The surface area of a rectangular solid is \(108 \mathrm{cm}^{2} .\) The height of the solid is \(4 \mathrm{cm}\) and the length is \(6 \mathrm{cm} .\) Find the width of the rectangular solid.
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