How to Calculate Area | Learn how to calculate area and apply it in the real world

Applying Area to the Real World for Kids Hey kids! You may have seen our video, Introduction to Perimeter and Area, in which we explain the basics about those two measurements. In the video, we demonstrate that perimeter is a measurement of the outside line of a shape or space, and area is a measurement of the space inside. But guess what? There's so much more to measuring and understanding area than you might think, and in this video, we dive deeper. Let's start by reintroducing you to what area is. Think about all the spaces around you, your yard, a nearby road, the inside of your school, the field inside a stadium, or the space inside a restaurant. All of those 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, big or small. One thing to remember is that area is always measured in squares. So, for example, the area of a space can be 10 square millimeters, 10 square inches, 10 square feet, 10 square miles, and so on. See this figure? It is a square, meaning all the sides are the same length. The length of each side is one inch, meaning that its total area measures one square inch, side times side, or one times one. Square inches are used to measure the area of things like pieces of paper, books, small tables, and other small surfaces like that. What else do you think you can measure in square inches? This is a square foot. A square foot has equal lengths of one foot or 12 inches. Square feet are used to measure the area of larger spaces like rooms or insides of buildings or backyards. The area of one square foot equals to 144 square inches, 12 inches times 12 inches. In feet, one square foot, one foot times one foot. Remember, we measure how much space we have in the inside of a figure. One square yard has a length and width of one yard, which is three feet. Square yards are sometimes used to measure the area of carpeting. A square mile is much bigger with a length and width of one mile or 5,280 feet. Square miles are used to measure the areas of large spaces like towns and cities or oceans and lakes. Here are some examples that will help put the area into some perspective. You may have worked with grid paper. Grid paper has lines and squares drawn on the paper. A typical sheet of grid paper is 100 squares, meaning it takes 100 squares to cover the area inside its boundaries. If each square is one inch by one 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 then the room is 12 feet wide by 12 feet long. Multiply the sides together, 12 times 12 and you get 144 square feet. A football field's area is about 6,300 square yards. That means it would take 6,300 one-yard squares to cover an entire field. How much area do you think the United States has? If you guessed 3,500,000 square miles, then you're amazing. That's right. 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. See these three shapes? They all have the same area, 12 square units. It could be square inches, square feet, or square miles, depending on the units you're working with. Notice how all those shapes have an exact number of squares in them, so it's pretty easy to figure out their areas. For irregular shapes, squares may not match the shape outline exactly. You can still use squares to calculate the area, but you have to approximate or guess how many pieces, when put together, make a square. See this circle? It's close to 18 square units, and this six-sided figure is about 26 square units. But it's hard to be exact using squares. These shapes have different ways of calculating areas. For simple geometric shapes, like squares and rectangles, all you need are two measurements, width and length, or base and height. In width and length, you multiply the longer side by the shortest. In base or height, you multiply the bottom by how tall the shape is. When finding the area, you always multiply two sides for simple shapes. Can you think of some real-life situations in which you might need to calculate the area? How about when you're carpeting a room, or painting a wall, or building a road, putting up a wall, or installing siding? Figuring out the area is a handy thing to know how to do. 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 tell the construction crew. If the pool looked like this, with sides of 3 feet, 10 feet, 6 feet, 4 feet, and 15 feet, what would the area be? This kind of shape is called an irregular shape. In general, regular shapes are like squares or rectangles. Irregular shapes are made by combining different shapes. Our swimming pool, for example, has more than one shape. First, look at the shape. What two shapes do you see that make the swimming pool an L-shape? If you said two rectangles, you are exactly right. Separate the swimming pool down into these two rectangles. Rectangle A has a length of 10 feet and a width of 3 feet. Its area is 30 square feet, or 10 times 3. Rectangle B has a length of 12 feet and a height of 4 feet. Its area is 48 square feet, or 12 feet times 4 feet. To find the total area, you need one more step. You add the square feet of both the rectangles together. 30 square feet plus 48 square feet equals 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, to which your friends would say, too much information. Here's another example. Let's say a community wants to build a playground for the neighborhood kids, and they want to tell the people living there what its area will be. If the playground looks like this, you can easily see that 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 times 15, or 300 square feet. Next, to calculate the rest of the area, you'd have to know how to figure out the area of a triangle. If you think about it, a triangle is half a square or rectangle, right? So if you remember that simple fact, you'll quickly memorize the formula for finding its area. It's half the length of the base times the height. Taking our triangle here, with a base of 20 and a height of 10, the area would be one half of 20, which is 10 times 10, or 100 square feet. That means the total area of this playground is 300 plus 100, or 400 square feet. Most triangles, however, are not part of a rectangle. Most of the time, they're on their own. So if you want to find out their area, you'll just need to remember that the area is always calculated by multiplying half the base times its height. Check out these examples. This triangle has a base of 4 and a height of 5. Can you figure out its area? If you said 10, you're right. Half of 4 is 2 times 5, equals 10. How about this one? That's right, 30. Half of 10 is 5 multiplied by 6. That's 30. And this one? Take half of 7 and multiply it by 2, and you get 7. Notice how, when you have a right triangle, the height is the leg of the angle. For the other triangles, the height is shown using a dashed or dotted line that goes from the bottom to the top. Now that we've mastered the area of triangles, let's take a look at one more example of something you might want to calculate the area of. Let's say your neighbor is building a deck in her backyard, and she wants to know its area so she can order the wood for the floor. The deck is in the shape of a hexagon, but as you can see, it can be broken up into 6 triangles, which each have 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, and therefore all 6 triangles that make up the entire gazebo equal 36 square feet. She'll need to order 36 square feet of wood for the floor. It looks like you're getting the hang of the area, but before we send you off into the world to become an area calculating machine, there are a few other shapes we should probably cover, because the world is more than just rectangles, squares, and triangles, right? You've got trapezoids, parallelograms, rhombuses, or is it rhombi, and other quadrilaterals. All of these have an area, and all of them can be calculated. While it will take a while to learn all the formulas, here's a quick tutorial. A trapezoid has two bases, as seen here. To calculate its area, you need to add the two bases together and multiply that by half its height. This trapezoid's area is calculated by adding 6 to 4, which is 10, and then multiplying that by 5. The area is 50 square units. Take a look at this parallelogram. Looks like a tilted rectangle, doesn't it? To calculate its area, you'll need to multiply its base times its height. This parallelogram's area is just 8 times 7, or 56 square units. To figure out the area of a rhombus, you have to use its two diagonals. This rhombus has two diagonals of 6 and 8. The formula is to multiply them together and then take half. 6 times 8 is 48, and half of that equals 24 square units. Finally, the quadrilateral. First, draw a diagonal to turn it into two triangles. Then find the area of those two triangles separately and add them together. One half base times height plus one half base times height. The area of this quadrilateral would be one half of 10 times 4 plus one half of 10 times 7, or 20 plus 35, 55 square units. Phew! So there you have it. There's a lot to learn, but if you practice enough, you'll become an area-calculating master. No space will be too big, too small, or too complicated for you to figure out its area. I don't know about you, but I think figuring out the area is fun! Now get out there and become the best area-figurer you can be! Thanks for following Clarendon Learning. Be sure to subscribe. For more free resources, check us out at clarendonlearning.org.