Quickly calculate the area of any 4-sided figure, including squares, rectangles, parallelograms, kites, and rhombuses

If you're stuck on your geometry homework trying to figure out the area of a quadrilateral, you've come to the right place! Remember—the "area" of a shape is just how much 2-dimensional space it takes up. For some quadrilaterals, there's a handy formula you can use to calculate the area. But what if all the sides are different? Just divide it into triangles! Read on to follow along with some examples and see how this works.

Things You Should Know

  • Find the area of any quadrilateral by dividing it into 2 triangles. Then, find the area of each of those triangles using the formula (Area = 1/2 base times height) and add them together.
  • Use the formula (Area = length times width) to find the area of a square or rectangle.
  • Multiply the lengths of the 2 diagonal lines and divide by 2 to find the area of a rhombus or kite.
  • Give the area of any quadrilateral in units squared. The unit corresponds with the unit used for the lengths you multiplied to find the area.

Area of Square, Rectangle, and Rhombus Cheat Sheets

Area of Trapezoid and Kite Cheat Sheets

Section 1 of 7:

Square

  1. Use to find the area of a square. In the formula, "s" is the length of one side. Since all sides are equal, you only need the length of one of them to quickly find the area of any square. Then, express the area in units squared.
    • For example, if you have a square and the length of one side is , you would multiply to get .
    • Try it with a square that has sides long. Just multiply . That square has an area of . No matter what the unit is, it's always squared when you're talking about the area.
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Section 2 of 7:

Rectangle

  1. Use the formula to find the area of a rectangle. Since a rectangle has sides of 2 different lengths, you multiply one value by the other to find out how much space the rectangle covers. Just get the length of one of the short sides and one of the long sides.
    • For example, if your rectangle has a length of and a width of , your equation would be , which gives you an answer of .
    • What if your rectangle has bigger numbers? The formula still works the same way. For example, a rectangle with a length of and a width of would have an area of .
Section 3 of 7:

Parallelogram

  1. Find the area of a parallelogram with . A parallelogram has 2 parallel sides—those are the bases (b). The height (h) is the distance from one base to the other. Multiply those 2 values together and you've got the area of a parallelogram.[1]
    • For example, say you have a parallelogram with a base length of and a height of . Plug your numbers into the equation to get , then simplify to find an area of .
    • Remember: the height isn't the same as the length of the side! It's the straight-line distance between the top and bottom bases.
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Section 4 of 7:

Trapezoid

  1. Use to calculate a trapezoid's area. Since the 2 bases (b) of a trapezoid aren't the same length, the average is used for the area of this shape. Once you have the average length of the two bases, multiply that by the height (h)—the distance between the two bases—to easily find the area of a trapezoid.[2]
    • For example, say you've got a trapezoid with a bottom side of , a top side of , and a height of . Start by adding the length of the two bases: . Then, divide by to get the average length of the bases: .
    • You've taken care of the first part of the formula! Now all you have to do is multiply the average length of the bases, , by the height, : . The area of your trapezoid is .
Section 5 of 7:

Rhombus

  1. Get the area of a rhombus with . In this formula, and refer to the length of 2 diagonal lines that you'll draw inside the shape between the opposite corners. Get the length of each of those 2 diagonals, multiply them together, then divide by 2. You've got the area of a rhombus![3]
    • For example, say you have a rhombus with diagonals of and . You know that . Divide by . The area of your rhombus is .
    • What if the product of the diagonals is an odd number? No problem, just express your answer as a decimal. For example, a rhombus with diagonals of and has an area of .
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Section 6 of 7:

Kite

  1. Find the area of a kite with . A kite's orientation can throw you off because your "diagonal" lines (d1 and d2) might not look diagonal at all—they might actually be vertical and horizontal. But as long as they're connecting opposing corners, they're still called diagonals. Multiply them together and then divide by to get your area.
    • For example, say you have a kite with diagonals of and . Plug those values into the formula: . The area of your kite is .
Section 7 of 7:

Any Quadrilateral Shape

  1. 1
    Divide the quadrilateral into 2 triangles. If you draw a diagonal line from one corner to the other, you create 2 triangles within the quadrilateral. The 2 triangles might not be the same size, but they share a common base—the diagonal that divides the quadrilateral.[4]
    • If you're working on a homework problem, the diagonal line might already be drawn for you. In fact, if you have a quadrilateral with a diagonal line, that's a pretty big clue that you'll use triangles to find the area.
  2. 2
    Get the measurements for the base and heights of your triangles. To find the area of a triangle, you need to know the size of the base (b) and the height (h). Your diagonal line is serving as the base of your triangles, so they'll both have the same measurement for the base. They might not be the same height, though, depending on the quadrilateral. The height isn't the length of a side (unless you're working with a right triangle). It's the length from the base to the top point of the triangle.[5]
    • If you're working a problem for homework and you're not given any way to measure these values, you can't use triangles to find the area of that quadrilateral.
  3. 3
    Find the area of each triangle. Recall that the formula for the area of a triangle is . All you have to do is plug in the measurements you got for the base and the height, then simplify the equation to find the area of each triangle.[6]
    • For example, say you have a diagonal with a length of that forms 2 triangles that each have a height of . Your formula would be , which simplifies to . So your answer would be .
    • In this example, both triangles have the same area since they both have the same base and height.
  4. 4
    Add the areas of the 2 triangles together to get the area of the quadrilateral. Since you originally divided your quadrilateral into 2 triangles, all you have to do is add those 2 areas together and you'll have the total area of the quadrilateral. You could also think of the area of one of the triangles as being half the area of the quadrilateral.[7]
    • To return to the previous example, since each triangle has an area of , you would simply add to get .
    • Area is always expressed in square units. If the measurements in your original problem were meters, your answer would be .
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Community Q&A

  • Question
    Could I divide the quadrilateral into two triangles, find the area of each, and add them to find the area of the quadrilateral?
    Donagan
    Donagan
    Top Answerer
    Yes. If you know the base and height of each triangle, you can just add the two areas together. It's not always possible, however, to know the bases and heights.
  • Question
    How do I calculate the area of a parallelogram?
    Community Answer
    Community Answer
    Calculate as follows: Area = base multiplied by height.
  • Question
    How would I know the angle for quadrilateral?
    Donagan
    Donagan
    Top Answerer
    Assuming you're not given the angle(s), you either have to use a protractor or analyze the quadrilateral and use trigonometry.
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About This Article

David Jia
Co-authored by:
Academic Tutor
This article was co-authored by David Jia and by wikiHow staff writer, Jennifer Mueller, JD. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 1,688,310 times.
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Co-authors: 81
Updated: March 7, 2023
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Article SummaryX

Before you can find the area of a regular quadrilateral, start by identifying the type of quadrilateral in the problem, since different types of quadrilaterals require different equations. For rectangles or rhombuses, simply multiply the base by the height to find the area. For squares, multiply one side by itself to get the area. If you have a parallelogram, multiply the diagonals and divide by 2 to get the area. To find the area of a trapezoid, add the base and the height together, and divide that number by 2 times the height. If you want to find the area of an irregular quadrilateral, keep reading the article!

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