Area Calculator

Area Calculator

Knowing how to calculate the area of a shape can be helpful in a variety of personal and professional applications. Students use area in various math classes, while homeowners need area for completing tasks like painting or landscaping. On this page, you'll find all the resources you need to calculate the area of most conventional shapes, including formulas and detailed diagrams. To use the calculator, you'll just have to include a few relevant measurements.

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Why is area relevant?
Area is relevant because it tells you how much space an object takes up or how large it is. Without area, you wouldn’t know the difference between a football stadium (57,600 square feet) and a baseball diamond (8,100 square feet). But that’s not all, knowing the exact size of an area can be useful in many different situations.
If you are doing home renovations , the area can tell you how much material to buy and how much it will cost you. When you are painting your house, you will need to know the surface that needs covering so that you can purchase the right amount of paint. For other projects like landscaping, you’ll probably want to know how much area you want your deck to take up before you start building it. The more accurate you are with your calculations, the better you can estimate what you will need to get a certain job done.
Finding out the area of standard shapes like rectangles, triangles, and circles is quite easy. Then, once you get the basics down, you can divide odd surfaces into individual sections made of familiar shapes. For example, if you are repainting the exterior of your shed you can split most surfaces into triangles and rectangles to find out how much area you need to coat.
How is area measured?
You can measure area using different units of length or distance. The type of measurement you use will depend on the size of the project. Smaller crafts can be measured in millimeters, centimeters, or inches. Conversely, larger projects may require more significant measurements in feet, meters, or miles.
In mathematics , the area of a figure identifies the number of square units that it covers. When a shape is drawn on a grid, you can find the area by counting the number of squares inside the form. The example below uses a grid, which has squares that measure 1cm on each side. That means each square on the grid is one square centimeter or abbreviated, 1 cm 2 .
Square Grid
If you count the squares in the example, you will arrive at 9. That means the area of this shape is 9 square centimeters or 9 cm2. Counting squares on a grid can work for all shapes as long as the grid size is labeled. However, if you don’t have a grid, you can figure out the area of a surface by taking some measurements and following a formula.
The formula changes based on the type of shape you are assessing. For example, getting the area of a triangle is different from other shapes like rectangles, trapezoids, or circles. For complex figures, you will have to divide the structure into smaller individual sections and may need multiple formulas to calculate the total area.
If any of this sounds confusing, don’t worry. Below, you can follow the different methods to find the area of standard shapes. Just select a subheading to expand the information and view the diagrams we have provided.
Squares, rectangles, and parallelograms
Area calculations are most commonly applied to squares and rectangles. Most rooms, walls, and houses are frequently composed of a series of squares and rectangles. Even bridges, buildings, and boxes use this common shape in their infrastructure.
When checking a shape, it’s important to measure all of the sides. If a figure looks like a square, you may find that it is actually a rectangle after charting its dimensions. Once you have measured the sides of your space accurately, just multiply the length (or height) by the width to find the area.
⦁ Area of a rectangle = height x width
Please see the following diagram for an example of an area calculation.
Squares and rectangles
When it comes to estimating the section of your home you want to do renovations, finding the total area may take a few more steps. When the walls of a room or space do not line up correctly, you could divide it into smaller individual sections. Then by adding up the sections, you can find out the total area. See the diagram below.
Rectangles
By plugging the numbers into the formula, you can quickly solve for the area. The area of A is 40m 2 , while the area of B is 150m 2 . When you add the sections together, the total area of the figure sums up to 190m 2 .
Triangles
When figuring out the area of a triangle, it can be helpful to think of a triangle as half of a square or rectangle. If you know the dimensions of the figure, or can measure it out, it is easy to calculate. Just multiply the base by the height, and divide by two to get your result.
⦁ Area of a triangle = (base x height) ÷ 2
The height of a triangle is measured as the line from the apex to the base, which forms a 90-degree angle. Please see the following diagram for an example of an area calculation.
Triangle
This type of calculation could be useful when working out how much paint you will need to freshen up the outdoor paneling of a shed or house. You can divide the face of the structure into a rectangle and triangle to find the total area. Follow along with the example below.
House area
To figure out the surface area of the face of the home, you will need to take a few measurements. First, you need the height of the apex, from the base up to the roof. Then you need the height of the vertical walls and the width of the building.
The diagram can be split into two shapes, a rectangle, and a triangle. Since you measured the height of the apex and the vertical walls, you can quickly find out the missing height of the triangle (area A). Just subtract the vertical walls from the height of the apex. Using the above example, 14m minus 6m equals 8m. The resulting 8m is the height of the upper triangle.
You can now work out the surface area of the wall.
Area A= (base x height) / 2
Area A= (12m x 8m) / 2
Area A= 96m/2
Area A= 48m 2
Area B= width x height
Area B= 12m x 6m
Area B= 72m 2
Total area= area of A + area of B
Total area= 48m 2 + 72m 2
Total area= 120m 2
So, how much paint would you need?
Well, a gallon of paint can cover approximately 250 square feet of coarse surface, like the outdoor paneling of a house. The total area in our example is 120m2, which converts to approximately 394 square feet. That means for one coat of fresh paint, you would need to purchase 2 gallons.
But don’t forget – in a real-life situation you would have to subtract any space where there is a door or windows to get an accurate area estimation.
Circle
If you are landscaping, you may need to calculate the area of a circle. You may also need to know the area of any circular windows to subtract from other surface calculations. For any designs or spaces that are circular, you can get the area by multiplying 3.1416 ( π ) by half of the diameter, squared .
⦁ Area of a circle= 3.1416 x (diameter ÷ 2) ^ 2
Please see the following diagram for an example of an area calculation.
Circle area
The more decimal points you use for Pi, the more accurate your calculations will be.
Trapezoid
A trapezoid is a variation of a rectangle with some triangular elements. Thus, the formula to find area uses aspects of both. You have to add the length of the base to the length of the top line. Divide that figure by two and multiply by the height of the shape to find the area.
⦁ Area of trapezoid= (a + b) ÷ 2 x h
Please see the following diagram for an example of an area calculation.
Trapezoid area
Sector
When you need to know the space in a section of a circle, like a shape that resembles a slice of pie- this is called a sector. You can calculate it using the radius of the circle, along with the degree of the central angle or the length of the arc.
⦁ Using the central angle:
Area of sector
⦁ Using the arc length:
Area of sector
Please see the following diagram for an example of an area calculation using both formulas.
Circles
Ellipse : An ellipse differs from a circle in that the major and minor axes are not equal. When this is the case, the shape forms an oval. Finding the area of an ellipse is very simple, you just need to measure the radius according to each axis.
⦁ Area of an ellipse or oval = π x a x b
Please see the following diagram for an example of an area calculation.
Ellipse area
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