Problem 556 - Prealgebra

Question

Roofing Lewis needs to put new shingles on his roof. The roof is a rectangle, 30 feet by 24 feet. What is the area of the roof?

Step-by-Step Solution

Answer

The area of the roof is 720 square feet.

Step 1: Understand the Shape

Identify that the roof is a rectangle with given dimensions: length = 30 feet and width = 24 feet.

Step 2: Recall the Area Formula

Remember that the area of a rectangle can be found using the formula: \[ \text{Area} = \text{length} \times \text{width} \]

Step 3: Substitute the Values

Substitute the length and width into the area formula: \[ \text{Area} = 30 \text{ ft} \times 24 \text{ ft} \]

Step 4: Calculate the Area

Perform the multiplication to find the area: \[ \text{Area} = 720 \text{ square feet} \]

Step 5: State the Final Answer

The area of the roof is 720 square feet.

Key Concepts

rectangle area formula

To calculate the area of a rectangle, we use a simple formula that every student should remember. The formula is \( \text{Area} = \text{length} \times \text{width} \).
This means to find the area of a rectangle, just multiply its length by its width.
Let's break it down:

• Length: This is the measurement of one of the longer sides of the rectangle.
• Width: This is the measurement of one of the shorter sides of the rectangle.

By knowing these two measurements, anyone can find the area. It's a fundamental concept in geometry that applies to many practical situations, like roofing! In the provided problem, the length is 30 feet and the width is 24 feet. Plugging these values into the formula gives us the area.

multiplication

Multiplication is one of the basic operations in mathematics. It’s a way to find the total of adding a number repeatedly.
In our roofing problem, we need to multiply the length of the roof by its width to get the area. Here's a simple example to understand:

• If you have 4 apples and you want 5 such groups of apples, you multiply 4 by 5 to get 20 apples.

Similarly, for the roof, you use multiplication to find the area:
\( 30 \text { ft} \times 24 \text { ft} = 720 \text{ square feet} \)
Multiplication helps us find how many square feet of shingles Lewis needs. By mastering multiplication, you can solve many such problems.

geometry basics

Geometry is the branch of mathematics that deals with shapes, sizes, and properties of space.
Some basic concepts include points, lines, and shapes like rectangles.
Understanding the basics of geometry helps us measure and calculate areas and volumes. Let's focus on some important points about rectangles:

• Rectangle: A four-sided shape with opposite sides that are equal and parallel and all angles being right angles.

From the problem, our shape is a rectangle. Knowing that its opposite sides are equal allows us to use the length and width measurements confidently in our calculations.
Geometry is essential for practical tasks like figuring out how many shingles are needed for a roof!