ClassX Video Lessons How to Calculate Area | Learn how to calculate area and apply it in the real world
Hello, everyone! Today, we’re going to learn about something called “area.” You might have heard about it before when we talked about perimeter and area. Perimeter is the distance around a shape, like a fence around a yard. Area, on the other hand, is all about the space inside that shape. Let’s dive in and explore more about area!
Think about all the spaces you see every day: your backyard, the classroom, a soccer field, or even a restaurant. All these spaces have an area. Area is the amount of space inside the boundary of a flat shape. It can be big or small, and we measure it in square units. For example, we might say something has an area of 10 square inches or 10 square feet.
Let’s look at some examples of square units:
Imagine you have a piece of grid paper with 100 squares. If each square is 1 inch by 1 inch, the paper’s area is 100 square inches. Now, think about a small room that’s 12 feet by 12 feet. Its area is 144 square feet because 12 times 12 equals 144.
What about a football field? Its area is about 6,300 square yards. That’s a lot of space!
To find the area of a shape, you count how many square units fit inside it. For simple shapes like squares and rectangles, you multiply the length by the width. For example, if a rectangle is 10 feet long and 3 feet wide, its area is 30 square feet (10 x 3).
For irregular shapes, like an L-shaped pool, you can break them into smaller rectangles. Add the areas of these rectangles to find the total area.
Knowing how to calculate area is super useful! You might need it when:
For example, if you want to build a playground, you can break it into shapes like rectangles and triangles to find the total area.
Besides squares and rectangles, there are other shapes like trapezoids, parallelograms, and rhombuses. Each has its own way to calculate area:
Learning about area is fun and useful! With practice, you’ll be able to calculate the area of any shape you encounter. Thanks for learning with us, and keep exploring the world of math!
Area Hunt: Go on an “Area Hunt” around your home or classroom. Find different objects or spaces, like a book, a table, or a small rug. Use a ruler or measuring tape to measure the length and width of each object in inches or feet. Calculate the area by multiplying the length by the width. Write down your findings and compare the areas of different objects. Which one has the largest area? Which one has the smallest?
Build Your Own Shape: Use graph paper to draw different shapes, such as rectangles, squares, or even L-shaped figures. Color in the squares inside each shape to visualize the area. Count the number of squares to find the area of each shape. Try creating a shape with a specific area, like 20 square units. How many different shapes can you make with the same area?
Real-Life Area Application: Think about a room in your house that you would like to redecorate. Measure the length and width of the room in feet. Calculate the area to find out how much carpet or paint you would need. Discuss with a family member how knowing the area helps in planning and buying the right amount of materials. Can you think of other situations where knowing the area would be helpful?
Sure! Here’s a sanitized version of the transcript, removing any informal language and ensuring clarity:
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Applying area to the real world for children.
Hello, kids! You may have seen our video introduction to perimeter and area, in which we explain the basics of these two measurements. In this video, we will demonstrate that perimeter measures the outside line of a shape or space, while area measures the space inside. However, there is much more to understanding area than you might think, and in this video, we will explore it in greater depth.
Let’s start by reintroducing you to what area is. Think about all the spaces around you: your yard, a nearby road, inside your school, the field inside a stadium, or the space inside a restaurant. All of these spaces can be measured by calculating their areas. Simply put, the area is the amount of space inside the boundary of a flat, two-dimensional object, whether it is big or small.
One important thing to remember is that area is always measured in square units. For example, the area of a space can be 10 square millimeters, 10 square inches, 10 square feet, 10 square miles, and so on.
Consider this figure: it is a square, meaning all the sides are the same length. If the length of each side is 1 inch, then its total area measures one square inch (1 inch x 1 inch). Square inches are used to measure the area of items like pieces of paper, books, small tables, and other small surfaces.
Next, we have a square foot. A square foot has equal lengths of one foot (12 inches). Square feet are used to measure the area of larger spaces, such as rooms, buildings, or backyards. The area of one square foot equals 144 square inches (12 inches x 12 inches).
A square yard has a length and width of 1 yard (3 feet). Square yards are sometimes used to measure the area of carpeting. A square mile is much larger, with a length and width of 1 mile (5,280 feet). Square miles are used to measure large areas, such as towns, cities, oceans, and lakes.
Here are some examples to help put area into perspective. You may have worked with grid paper, which has lines and squares drawn on it. A typical sheet of grid paper contains 100 squares, meaning it takes 100 squares to cover the area inside its boundaries. If each square is 1 inch by 1 inch, then the area of the paper is 100 square inches (100 inches squared).
The area of a small room in a house might be 144 square feet. If the room is square, then it is 12 feet wide by 12 feet long. Multiplying the sides together (12 x 12) gives you 144 square feet. A football field’s area is about 6,300 square yards, which means it would take 6,301 square yards to cover the entire field.
How much area do you think the United States has? If you guessed 3,500,000 square miles, then you are correct! It would take 3,500,000 one-mile squares to cover all the land in the U.S.
To find the area, you simply count the number of square units of a figure. Consider these three shapes; they all have the same area of 12 square units. It could be square inches, square feet, or square miles, depending on the units you are working with. Notice how all those shapes have an exact number of squares in them, making it easy to figure out their areas.
For irregular shapes, the squares may not match the shape outline exactly, but you can still use squares to estimate the area. For example, this circle is close to 18 square units, and this six-sided figure is about 26 square units. However, it can be challenging to be exact with squares.
For simple geometric shapes like squares and rectangles, you only need two measurements: width and length, or base and height. To find the area, you multiply the longer side by the shorter side.
Can you think of some real-life situations where you might need to calculate area? For example, when carpeting a room, painting a wall, building a road, or installing siding. Knowing how to calculate area is a useful skill.
Let’s say you want someone to build an L-shaped swimming pool in your backyard. You would need to know the area of the pool to inform the construction crew. If the pool has sides measuring 3 feet, 10 feet, 6 feet, 4 feet, and 15 feet, what would the area be? This shape is called an irregular shape.
In general, regular shapes are like squares or rectangles, while irregular shapes are made by combining different shapes. Our swimming pool, for example, consists of two rectangles.
Rectangle A has a length of 10 feet and a width of 3 feet, giving it an area of 30 square feet (10 x 3). Rectangle B has a length of 12 feet and a height of 4 feet, resulting in an area of 48 square feet (12 x 4). To find the total area, you add the areas of both rectangles together: 30 square feet + 48 square feet = 78 square feet.
Now, every time you take a swim, you can say, “If you need me, I’ll be doing laps in my 78 square foot pool.”
Here’s another example: let’s say a community wants to build a playground for the neighborhood kids and inform the residents about its area. If the playground looks like this, you can break it down into one rectangle and one triangle. The rectangle is 20 feet long and 15 feet wide, making its area 20 x 15 = 300 square feet.
To calculate the area of the triangle, remember that a triangle is half of a rectangle. If the triangle has a base of 20 feet and a height of 10 feet, the area would be (1/2) x 20 x 10 = 100 square feet. Therefore, the total area of the playground is 300 + 100 = 400 square feet.
Most triangles, however, are not part of a rectangle. To find their area, remember that the area is calculated by multiplying half the base by its height.
Now that we’ve mastered the area of triangles, let’s look at one more example. Suppose your neighbor is building a deck in her backyard and wants to know its area to order the wood for the floor. The deck is in the shape of a hexagon, which can be broken up into six triangles, each with a base of 4 feet and a height of 3 feet.
Using our formula for the area of a triangle, we can quickly calculate that the area of each triangle is 6 square feet. Therefore, all six triangles that make up the entire deck equal 36 square feet. She will need to order 36 square feet of wood for the floor.
It looks like you are getting the hang of calculating area! However, before we conclude, there are a few other shapes we should cover, as the world includes more than just rectangles, squares, and triangles.
You also have trapezoids, parallelograms, rhombuses (or rhombi), and other quadrilaterals, all of which have areas that can be calculated. While it may take time to learn all the formulas, here’s a quick overview:
– A trapezoid has two bases. To calculate its area, add the two bases together and multiply by half its height. For example, if the bases are 6 and 4, and the height is 5, the area is (6 + 4) x (1/2) x 5 = 50 square units.
– A parallelogram looks like a tilted rectangle. To calculate its area, multiply its base by its height. For example, if the base is 8 and the height is 7, the area is 8 x 7 = 56 square units.
– To find the area of a rhombus, use its two diagonals. If the diagonals are 6 and 8, the formula is (6 x 8) / 2 = 24 square units.
– For a quadrilateral, first draw a diagonal to divide it into two triangles. Then find the area of each triangle separately and add them together.
For example, if one triangle has a base of 10 and a height of 4, and the other has a base of 10 and a height of 7, the area would be (1/2) x 10 x 4 + (1/2) x 10 x 7 = 20 + 35 = 55 square units.
In conclusion, there is much to learn about area, but with practice, you can become proficient at calculating it. No space will be too big, too small, or too complicated for you to figure out its area.
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