This article was co-authored by David Jia. 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.
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Finding the area of a square is easy as long as you know the length of its side, perimeter, or diagonal. Here's how to do it.
Steps
Using the Length of a Side
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1Write it down. Let's say you're working with a square with a side length of 3 centimeter (1.2 in). Write it down.
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2Understand the formula for the area of a square(Area=side^2). To calculate the area of any rectangle, you need to multiply its length by width. But since all squares have equal length sides, you can just multiply the distance by itself. If the length of a side of a square is 3 centimeter (1.2 in), then you just have to square 3 centimeter (1.2 in) to find the area of a square. 3 centimeter (1.2 in) x 3 centimeter (1.2 in) = 9 cm2.[1]Advertisement
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3Be sure to state your answer in square units. Then you're done.[2]
- Squaring the side of a square is the same thing as multiplying the square's height times its base.
Using a Known Diagonal
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1Take the measurement of the length of the diagonal of the square.
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2Understand the formula for the area using a known diagonal. Area = (diagonal^2)/2.[3]
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3Multiply the length of this diagonal's measurement by itself. Square the length of the diagonal. Let's say you're working with a square with a diagonal that is 5 centimeter (2.0 in) long. Now, square this number. 5 centimeter (2.0 in) x 5 centimeter (2.0 in) = 25 cm2.
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4Divide the current number by 2. Continuing the calculation, 25 cm2 is divided by 2. This gives 12.5 cm2. You're done.
Using a Known Perimeter
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1Multiply the perimeter by 1/4 to find the length of a side. This is the same as dividing the perimeter by 4. Since there are four sides to a square and each side is of equal length, you can find the length of a square just by dividing the perimeter by 4. Let's say the perimeter of the square you're working with is 20 centimeter (7.9 in). Just multiply 20 centimeter (7.9 in) by 1/4: 20 centimeter (7.9 in) x 1/4 = 5 centimeter (2.0 in). You know that the length of a side of the square is 5 centimeter (2.0 in).[4]
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2Multiply the length of the side by itself. Square the length of the side. Now that you know that the length of a side is 5 centimeter (2.0 in), you can square it to get the area of the square. Area = (5 cm)2 = 25 centimeter (9.8 in).2[5]
Community Q&A
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QuestionIf the area of the square is 9 cm, what is the volume of the cube?
DonaganTop AnswererTake the square root of 9 and cube it. The answer will be expressed in cm³. -
QuestionWhat is the formula to calculate the area of an isosceles triangle that has a base and equal sides?
Community AnswerMultiply the length of the base of the triangle by 0.5, and then multiply the length from the base to the highest point of the triangle. A = 0.5 x b x h. -
QuestionA square is 1 cm by 1 cm; what is the area?DonaganTop AnswererMultiply 1 cm by 1 cm: the area is 1 square cm.
References
- ↑ https://www.mathplanet.com/education/pre-algebra/inequalities-and-one-step-equations/calculating-the-area-and-the-perimeter
- ↑ https://www.mathplanet.com/education/pre-algebra/inequalities-and-one-step-equations/calculating-the-area-and-the-perimeter
- ↑ https://www.youtube.com/watch?v=OC2rMWzc-I8
- ↑ https://sciencing.com/area-square-using-its-perimeter-7991359.html
- ↑ https://sciencing.com/area-square-using-its-perimeter-7991359.html
About This Article
To find the area of a square, use the formula a = side^2, where side is the length of one of the sides of the square. If you only know the perimeter of the square, you can find the area by dividing the perimeter by 4, which will give you the length of each side, and then plugging the side into the formula a = side^2. If you want to learn how to find the area of a square if you only know the length of a diagonal, keep reading!
