Problem 66 - Prealgebra

Question

Find the area and perimeter for a rectangle if the length and width are as given below. \(I=210\) meters, \(w=120\) meters

Step-by-Step Solution

Answer

The perimeter is 660 meters, and the area is 25,200 square meters.

Step 1: Understand the Rectangle's Dimensions

Identify the length and width of the rectangle. For this problem, the length \(l\) is given as 210 meters and the width \(w\) is 120 meters.

Step 2: Calculate the Perimeter

The formula for the perimeter \(P\) of a rectangle is given by \(P = 2l + 2w\). Substitute \(l = 210\) and \(w = 120\) into the formula. \[ P = 2(210) + 2(120) = 420 + 240 = 660 \] Thus, the perimeter of the rectangle is 660 meters.

Step 3: Calculate the Area

The formula for the area \(A\) of a rectangle is \(A = l imes w\). Substitute \(l = 210\) and \(w = 120\) into the formula. \[ A = 210 imes 120 = 25200 \] Thus, the area of the rectangle is 25,200 square meters.

Key Concepts

Area Calculation

Calculating the area of a rectangle is a straightforward process that involves determining the amount of space encompassed within its boundaries. To determine this, you need to know the rectangle's length and width.

The formula for calculating the area of a rectangle is:- \( A = l \times w \) - Where \( A \) is the area, \( l \) is the length, and \( w \) is the width.To calculate, simply multiply the length by the width. Let's apply this to our example where the length \( l = 210 \) meters and the width \( w = 120 \) meters.- Substitute these values into the formula: - \( A = 210 \times 120 \) - Resulting in an area of: 25,200 square meters.Remember, the area measures how much flat space is enclosed by the rectangle in two dimensions.

Perimeter Calculation

The perimeter of a rectangle is the total distance around the outer edge. Calculating the perimeter helps you know how much material you would need to go around the rectangle, like a fence or border.

The formula for the perimeter is:- \( P = 2l + 2w \) - Where \( P \) is the perimeter, \( l \) is the length, and \( w \) is the width.To find the perimeter, you add together twice the length and twice the width. For our example rectangle:- Substitute the length \( l = 210 \) meters and width \( w = 120 \) meters into the formula: - \( P = 2(210) + 2(120) \) - This gives a perimeter of: 660 meters.Perimeter is a key concept in understanding how much boundary space surrounds a shape.

Geometry for Beginners

Geometry, in the simplest terms, is a branch of mathematics that studies the properties and relations of points, lines, surfaces, and solids. Rectangles are a fundamental shape studied in geometry.

Some basics about rectangles that beginners should keep in mind:

• A rectangle has four sides, with opposite sides being equal in length.
• It contains four right angles, meaning every angle is 90 degrees.
• The two main properties used often are area (the space within) and perimeter (the boundary length).

Understanding geometry concepts such as area and perimeter is crucial as they apply to various real-world problems, from determining the size of a garden plot to planning the layout of a building.

By grasping these fundamental geometric concepts, you will be better equipped to understand more complex shapes and computations in the future.