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The term
“area” in mathematics refers to the amount of space that a two-dimensional
shape occupies. Area can be represented by centimeters, meters, feet, and other
units of measurement. Because not all geometric 2D shapes have the same number
of sides, a different formula is required for calculating the area for each
shape. This page will focus on finding the area of seven of the most common 2D
shapes. These include rectangle, square, circle, triangle, trapezoid, ellipse, and parallelogram.
Because these formulas involve 2D shapes, all area calculations have a “2” exponent (also known as a superscript or power) to indicate that the shape has two sides.
The formula for finding the area of a rectangle is A = w x l, where “w” represents the width and “l” represents the length.
Example:
A = 32 x 52
A = 1664 ft2
Use the A = a2 formula to find the area of a square. The “a” represents one side of the square. Since a square has four equal sides, having the measurement of one side gives you the measurement for the others.
Example:
A = a2
A = 122
A = 144 in2
To find the area of a circle, use the following formula: A = πr2. The “r” in this formula represents the radius
of the circle.
Example:
A = π 2
A = 14π 2
A = π 196
A ≈ 615.75 m2
The standard formula for finding the area of a triangle is where “b” represents
the base and “h” represents the height.
Example:
A = 58.5 cm2
Use
the formula to find the
area of a trapezoid. In this formula, “a” represents the shorter base (top),
“b” represents the longer base (bottom), and “h” represents the height.
Example:
A = 36 yd2
An
ellipse is similar to a circle in its appearance, except that it is precisely
defined. It is, essentially, a circle, stretched horizontally, with two
symmetrical axes. An oval is not precisely
defined. To calculate the area of an ellipse, use the A = π a x b formula. The “a”
represents the horizontal axis while the “b” represents the vertical axis.
Example:
A
= π a x b
A
= π x 4 x 15
A
≈ 12.566 x 15
A
≈ 188.5 ft2
The
formula for calculating the area of a parallelogram is A = b x h. The “b” represents the base, and the “b” represents the
height.
Example:
A
= b x h
A
= 23 x 11
A = 253 in2
Area Formulas of Common Geometric Shapes
The chart below provides the area formula of the
aforementioned 2D shapes, in addition to some other common ones.
HeyTutor looked at COVID-19 vaccination rates among children in every state in the U.S. and Washington D.C.
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A metaphor draws a direct comparison between two seemingly unrelated ideas. Used in many forms of writing as well as other forms of creative expression, metaphors can add meaning.