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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
There are 12 references cited in this article that you can view at the bottom of the page.
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There are many reasons why you might want to know the area of some geometry. Whether you’re doing your homework or want to know how much paint you need to buy to repaint a room, wikiHow can help no matter what! Start with Step 1 below to learn how to calculate the area of geometric shapes.
Steps
Squares, rectangles, and parallelograms
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Measure width and height. First, you need to find the width and height of the shape (in other words, find the measure of two adjacent sides). [1] X Research Source
- For a parallelogram, you need to use the base edge and height, which is similar to the concept of width and height.
- In practice, you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Multiply the lengths of the sides. For example, if you have a rectangle with a height of 16 cm and a width of 42 cm, you will multiply by 16 x 42. [2] X Research Source
- If you are calculating the area of a square, you can save time by using a calculator and squaring one side. If the side length is 4 cm, then press the number 4 and then press the square button on the calculator to get the answer. To square is to multiply the number by itself.
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Find the results. The result from the multiplication is the area of the figure, written with “square units”. Hence the area of the rectangle will be 672 square centimeters.
- The unit of area is also abbreviated as a small 2 above the length symbol to replace the word “square”.
Trapezoid
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Find the lengths of the sides. You need the lengths of the bottom edge, top edge, and height. The bottom and top edges are two parallel sides, and the altitude is the perpendicular to those two sides. [3] X Research Sources
- In practice, you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Add the measurements of the bottom and top edges. Let’s say our trapezoid has a top edge of 5 cm and a bottom edge of 7 cm. The result of the addition is 12.
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Multiply that value by 1/2. The result of this calculation is 6.
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Multiply that value by the height. For this trapezoid, let’s assume a height of 6 cm. The result of the calculation is 36. [4] X Research Source
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Find the results. The number you get after multiplying by the height is the area of the trapezoid. Therefore, a 5x6x7 trapezoid has an area of 36 square centimeters.
Circle
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Find the radius. To find the area of a circle, you need the length of the radius. It is the length of the line segment connecting the center of the circle to a point on the circle. You can also find the radius by dividing the diameter in half. [5] X Research Sources
- In practice, you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Take the square of the radius. Multiply the radius length by itself. Let’s say we have a radius length of 8 meters. The result of the multiplication is 64.
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Multiply by pi. Pi (π) is a very commonly used number in many calculations. If you are using a calculator, press the pi button for accurate results. If you don’t have a calculator, you can round off pi (ignore the decimals) and simply multiply by 3.14159. The result of the calculation is 201.06176. [6] X Research Sources
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Find the results. So we have the area of the circle is 201.06176 square meters.
Fan shape
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Find the required measurements. The fan is part of the circle and looks like a hand fan. You need to know the radius of the original circle, or one side of the “fan”, and the angle formed by the two sides of the fan. Let’s say we have a radius of 14 cm and an angle between the two radii of 60 degrees. [7] X Research Sources
- In practice, you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Take the square of the radius. Multiply the radius length by itself. The result of this multiplication is 196 (14×14).
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Multiply by pi. Pi (π) is a very commonly used number in many calculations. If you are using a calculator, press the pi button for accurate results. If you don’t have a calculator, you can round off pi (ignore the decimals) and simply multiply by 3.14159. The result of this calculation is 615,75164. [8] X Research Sources
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Divide the angle by 360. Now you need to take the measure of the angle divided by 360 (which is the number of degrees of a circle). For this problem, we get 0.166. It’s actually a periodic number, but we’ve rounded it off to make it easier to calculate.
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Multiply this value by the previously obtained value. Multiply the number you get when you divide by 360 by the number you found earlier after multiplying by pi. The result of the calculation is 102,214.
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Find the results. So we have the area of the fan shape is 102.214 square cm.
Ellipse
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Find the measurements. To calculate the area of an ellipse, you need to know two “radii” that can be thought of as half of the ellipse’s width and height. These are the lines from the center of the ellipse to the midpoint of the long side and from the center of the ellipse to the midpoint of the short side. These two segments will be perpendicular to each other.
- In practice, you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Multiply the two radii. Let’s say our ellipse has a width of 6 cm and a height of 4 cm. The two radii will be 3 cm and 2 cm respectively. Now we multiply these two numbers together to get 6 (3×2).
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Multiply that value by pi. Pi (π) is a very commonly used number in many calculations. If you are using a calculator, press the pi button for accurate results. If you don’t have a calculator, you can round off pi (ignore the decimals) and simply multiply by 3.14159. The result of this multiplication is 18.84954.
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Find the results. So the area of the ellipse is 18.84954 square centimeters.
Triangle
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Find the measurements. You need to know the measure of the base and height of the triangle. The base edge is any side of the triangle at which the altitude can be calculated. Suppose we have a triangle with base side 3 meters and height 1 meter. [9] X Research Source
- In practice you will have to measure yourself, but for homework, the teacher has given these measurements on the picture.
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Multiply the bottom edge by the height. The result of the calculation is 3 (3×1). [10] X Research Source
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Multiply that value by 1/2. The result is 1.5.
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Find the results. So the area of the triangle is 1.5 square meters.
Complex shapes
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Divide the shape into several parts. To calculate the area of complex shapes, you must divide them into several smaller shapes that have the same standard geometry as above. With this example exercise, you probably already see what the shapes are, but in reality you need to break them down into lots of smaller shapes to get the exact area. [11] X Research Source
- You will initially find right angles and parallel sides. It is the basis of many shapes.
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Calculate the area of the individual shapes. Use the instructions above to find the area of different shapes.
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Add the shapes together. Add the areas of the shapes together to get the area of the original shape.
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Use other methods. There are other tips for calculating area, depending on your shape. You can also add an imaginary area to get a standard geometry, then subtract the area of the imaginary from the total area.
Advice
- Use this calculator if needed and when you want to see how the problem is solved.
- Ask your friends for help if you get stuck!
Warning
- Remember to use the same unit of measure to avoid confusing numbers!
- You’d better check the results again after the calculation is done!
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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
There are 12 references cited in this article that you can view at the bottom of the page.
This article has been viewed 6,075 times.
There are many reasons why you might want to know the area of some geometry. Whether you’re doing your homework or want to know how much paint you need to buy to repaint a room, wikiHow can help no matter what! Start with Step 1 below to learn how to calculate the area of geometric shapes.
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