How to Find Area

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Area is a measurement of the amount of space inside a two-dimensional figure. Sometimes, finding area can be as simple as simply multiplying two numbers, but oftentimes it can be more complicated. Read this article for a brief overview for the following shapes: quadrilaterals, triangles, circles, surface areas of pyramids and cylinders, and the area under an arc.

Method 1
Method 1 of 10:

Rectangles

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  1. Because rectangles have two pairs of sides of equal length, label one side as the base (b) and one side as the height (h). Generally, the horizontal side is the base and the vertical side is the height. [1]
  2. If the area of the rectangle is k, k=b*h. This means that the area is simply the product of the base and the height. [2]
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Method 2
Method 2 of 10:

Squares

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  1. Because squares have four equal sides, all of the sides should have this same measurement. [3]
  2. This is your area. [4]
    • This works because a square is simply a special rectangle that has equal width and length. So, in solving k=b*h, b and h are both the same value. So, you end up squaring a single number in order to find the area.
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Method 3
Method 3 of 10:

Parallelograms

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  1. Find the length of this base.
  2. Draw a perpendicular line to this base, and determine the length of this line between where it crosses the base and the side opposite to the base. This length is the height.
    • If the side opposite to the base is not long enough that the perpendicular line crosses it, extend the side along the line until it intersects the perpendicular line.
  3. [5]
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Method 4
Method 4 of 10:

Trapezoids

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  1. Assign these values to variables a and b.
  2. Draw a perpendicular line that crosses both parallel sides, and the length of the line segment on this line connecting the two sides is the height of the parallelogram (h). [6]
  3. [7]
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Method 5
Method 5 of 10:

Triangles

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  1. This is the length of one side of the triangle (the base), and the length of the line segment perpendicular to the base connecting the base to the opposite vertex of the triangle.
  2. [8]
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Method 6
Method 6 of 10:

Regular Polygons

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  1. Find the length of a side and the length of the apothem (the line segment perpendicular to a side connecting the middle of a side to the center. The length of the apothem will be assigned the variable a.
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Method 7
Method 7 of 10:

Circles

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  1. This is a line segment connecting the center to a point on the circle. By definition, this value is the same no matter what point you pick on the circle.
  2. [9]
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Method 8
Method 8 of 10:

Surface Area of a Pyramid

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  1. k=b*h
  3. the base and all the sides.
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Method 9
Method 9 of 10:

Surface Area of a Cylinder

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  3. A=πr^2. [10]
  4. The perimeter of a circle is P=2πr, so the area of the side is A=2πhr. [11]
  5. the two identical circular bases and the side. So, the surface area should be SA=2πr^2+2πhr.
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Method 10
Method 10 of 10:

The Area Under a Function

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Say you want to find the area under a curve and above the x-axis modeled by function f(x) in the domain interval x within [a,b]. This method requires knowledge of integral calculus. If you have not taken an introductory calculus course, this method may not make any sense.

  2. By the Fundamental Theorem of Calculus, given F(x)=∫f(x), ∫abf(x) = F(b)—F(a).
  3. The area under f(x) between x [a,b] is defined as ∫abf(x). So, A=F(b))—F(a).
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Community Q&A

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  • Question
    How do you find the area of a triangle?
    Community Answer
    The area of a triangle is one-half the product of the base and height. A = (bh) / 2. For example, if a triangle has a base of 8cm and a height of 5 cm, its area is [(8)(5)] / 2 = 40 / 2 = 20 square centimeters.
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      References

      1. ↑ https://www.khanacademy.org/math/cc-third-grade-math/imp-geometry/imp-multiply-to-find-area/a/area-rectangles-review
      2. ↑ David Jia. Academic Tutor. Expert Interview. 7 January 2021.
      3. ↑ https://www.cuemath.com/measurement/area-of-square/
      4. ↑ https://www.omnicalculator.com/math/square-area
      5. ↑ https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-parallelogram-area/a/area-of-parallelogram
      6. ↑ https://www.mathopenref.com/trapezoidarea.html
      7. ↑ https://www.varsitytutors.com/isee_middle_level_math-help/how-to-find-the-area-of-a-trapezoid
      8. ↑ https://www.omnicalculator.com/math/triangle-area
      9. ↑ https://www.mathsisfun.com/geometry/circle-area.html
      1. ↑ https://www.omnicalculator.com/math/surface-area-of-cylinder
      2. ↑ https://www.omnicalculator.com/math/surface-area-of-cylinder

      About This Article

      Article Summary X

      To find the area of a square, measure the length of any 1 of the sides, and multiply it by the same number to get the area. If your shape is a rectangle, start by finding the length of 1 horizontal side and 1 vertical side. Next, label the horizontal side as the base and the vertical side as the height. Then, multiply the base and height calculate the area. To learn more, including how to find the area for shapes like trapezoids and parallelograms, scroll down.

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