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Chapter 9: Problem 16

Find the area of the square. 18 yd on a side

Short Answer

Expert verified
324 square yards

Step by step solution

01

Identify the Side Length

First, identify the length of one side of the square. In this problem, the side length is given as 18 yards.
02

Recall the Formula for the Area of a Square

The area of a square can be found using the formula: \[ \text{Area} = \text{side length}^2 \]
03

Substitute the Side Length into the Formula

Substitute the given side length into the formula: \[ \text{Area} = 18^2 \]
04

Calculate the Area

Perform the calculation: \[ \text{Area} = 18 \times 18 = 324 \text{ square yards} \]

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Key Concepts

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

geometry
Understanding geometry is key when calculating the area of shapes like squares. Geometry is the branch of mathematics that explores properties and relationships of points, lines, surfaces, and solids.

In this context, we are focusing on a 2-dimensional shape, specifically a square. A square is a type of polygon with four equal sides and four right angles.

Knowing these properties is essential because they help us identify which formulas and mathematical operations apply. For squares, the key property to remember is that all four sides are of equal length.
area calculation
Calculating the area of a square is straightforward once you understand the concept of the area.

The area is a measure of the space enclosed within a shape. It's expressed in square units. For squares, this involves a very specific and simple formula

To calculate the area, you must first determine the length of one side. Once you have this measurement, you simply square it, or multiply it by itself.
mathematical formulas
Mathematical formulas are tools that make it easier to perform consistent calculations and solve problems quickly.

When it comes to finding the area of a square, you need to use the formula \( \text{Area} = \text{side length}^2 \).

This formula takes the length of one side and squares it. Squaring a number means multiplying it by itself, which can be written in equation form as follows: \[ \text{Area} = s \times s \] where \( s \) represents the side length.
squares
Squares have unique characteristics that make them easy to work with in geometry and area calculation.

A square has four equal sides and four 90-degree angles. These properties mean that once you know the length of one side, you immediately know the length of all its sides.

For example, in our problem, the side length is 18 yards. Using this, you can quickly find the area by squaring this length: \[ \text{Area} = 18^2 = 324 \text{ square yards} \].

This consistency is what makes working with squares so straightforward and predictable in mathematical problems.

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