How to Find Area

Co-authored by David Jia

Last Updated: December 3, 2024 Fact Checked

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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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]
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Multiply base times height to get the area. 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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David Jia
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Expert Interview. 7 January 2021.}
- For more extensive instructions, check out How to Find the Area of a Quadrilateral

Method 2

Method 2 of 10:

Squares

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Because squares have four equal sides, all of the sides should have this same measurement.^{[3]
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Square the length of the side. This is your area.^{[4]
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- 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.

Method 3

Method 3 of 10:

Parallelograms

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Find the length of this base.
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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.
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Plug the base and height into the equation k=b*h.^{[5]
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- For more extensive instructions, check out How to Find the Area of a Parallelogram

Method 4

Method 4 of 10:

Trapezoids

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Assign these values to variables a and b.
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]
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Plug these values into the formula A=0.5(a+b)h.^{[7]
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- For more extensive instructions, check out How to Calculate the Area of a Trapezoid

Method 5

Method 5 of 10:

Triangles

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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.
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To find the area, plug the base and height values into the equation A=0.5b*h.^{[8]
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- For more extensive instructions, check out How to Calculate the Area of a Triangle

Method 6

Method 6 of 10:

Regular Polygons

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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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Plug these values into the equation A=0.5a*p
- For more extensive instructions, check out How to Find the Area of Regular Polygons

Method 7

Method 7 of 10:

Circles

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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.
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Plug the radius into the equation A=πr^2.^{[9]
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- For more extensive instructions, check out How to Calculate the Area of a Circle

Method 8

Method 8 of 10:

Surface Area of a Pyramid

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k=b*h
the base and all the sides.

Method 9

Method 9 of 10:

Surface Area of a Cylinder

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A=πr^2.^{[10]
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The perimeter of a circle is P=2πr, so the area of the side is A=2πhr.^{[11]
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Add up all the areas: the two identical circular bases and the side. So, the surface area should be SA=2πr^2+2πhr.
- For more extensive instructions, check out How to Find the Surface Area of Cylinders

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.

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

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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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