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What is Area in Math? - Definition & Formula

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  • 0:05 Definition of Area
  • 0:35 Area Formulas
  • 1:47 Units of Area
  • 2:13 Finding the Area…
  • 2:50 Finding the Area of…
  • 5:07 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Area is the size of a two-dimensional surface. This lesson will define area, give some of the most common formulas, and give examples of those formulas. A quiz at the end of the lesson will allow you to work out some area problems on your own.

Definition of Area

The mathematical term 'area' can be defined as the amount of two-dimensional space taken up by an object. The use of area has many practical applications in building, farming, architecture, science, and even deciding how much paint you need to paint your bedroom. The area of a shape can be determined by placing the shape over a grid and counting the number of squares that the shape covers, like in this image:

Area can be determined using a grid.
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The area of many common shapes can be determined using certain accepted formulas. Let's take a look at the most common formulas for finding area.

Area Formulas

To find the area of a rectangle, you use this formula:

Area = length * width

The area of a square is found with this formula:

Area = s2, where s = side

The formula for the area of a triangle is:

Area = (1/2) b * h, where b = base and h = height

To find the area of a circle, use this formula:

Area = pi * r2, where r = radius

The area of a parallelogram is found using this formula:

Area = b * h, where b = base and h = vertical height

The formula for the area of a trapezoid is:

Area = (1/2) * (a + b) * h, where a =base 1, b = base 2, and h = vertical height

An ellipse's area is found this way:

Area = pi * a * b, where a = radius of major axis and b = area of minor axis

Units of Area

Finding the area of a shape always requires the multiplication of two lengths. In a square, it's side multiplied by side. In a circle, it's the radius squared. For an ellipse, it's the radius of the major axis multiplied by the radius of the minor axis. Due to this, the units given to area will always be squared (feet squared, inches squared, etc.). Anything multiplied to itself is squared, whether it is a number or not.

Finding the Area Example Problems

Let's practice finding the area with some example problems.

What is the area of a square with side length of 5 inches?

Remember, the formula for finding the area of a square is A = s2. The sides of this particular square are 5 inches. Plug that into the formula to get A = 52 = 25 in2.

What is the area of this parallelogram?

Parallelogram for example problem
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Remember, the formula is A = b * h. So, for this example, the area would be A = 3 * 12 = 36 mm2.

Finding the Area of Uncommon Shapes

If you are asked to find the area of an uncommon shape, it can be done by breaking the shape into more common shapes, finding the area of those shapes, and then adding the areas together. Let's look at some examples:

Find the area of this shape:

Shape for example problem
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The first step to solving this problem is to divide the shape into shapes we can find the area of easily. This shape can be divided into a triangle and a square.

To find area, divide uncommon shapes into common ones.
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