Area Of Two Dimensional Shapes

Perimeter and Surface Area Formulas

Perimeter is the distance around a shape while surface area is the surface area contained inside it. Daniel Grizelj / Getty Images

Updated on March 01, 2019

Perimeter and area formulas are mutual geometry calculations used in math and science. While it'south a good idea to memorize these formulas, here is a listing of perimeter, circumference, and surface surface area formulas to use as a handy reference.

Key Takeaways: Perimeter and Area Formulas

• The perimeter is the distance effectually the outside of a shape. In the special instance of the circle, the perimeter is likewise known as the circumference.
• While calculus may be needed to detect the perimeter of irregular shapes, geometry is sufficient for about regular shapes. The exception is the ellipse, simply its perimeter may be approximated.
• Area is a mensurate of the space enclosed within a shape.
• Perimeter is expressed in units of distance or length (e.thousand., mm, ft). Surface area is given in terms of square units of distance (e.thou., cm², ft²).

Triangle Perimeter and Surface area Formulas

A triangle has three sides. Todd Helmenstine

A triangle is a iii-sided closed effigy.
The perpendicular distance from the base to the opposite highest signal is called the height (h).

Perimeter = a + b + c

Expanse = ½bh

Square Perimeter and Surface Expanse Formulas

Squares are four-sided figures where each side is of equal length. Todd Helmenstine

A foursquare is a quadrangle where all iv sides (due south) are of equal length.

Perimeter = 4s

Area = s²

Rectangle Perimeter and Surface Area Formulas

A rectangle is a iv-sided figure with all interior angles are right angles and opposing sides have equal lengths. Todd Helmenstine

A rectangle is a special blazon of quadrangle where all the interior angles are equal to 90° and all reverse sides are the same length. The perimeter (P) is the distance effectually the outside of the rectangle.

P = 2h + 2w

Area = h x due west

Parallelogram Perimeter and Surface Expanse Formulas

A parallelogram is a quadrangle where contrary sides are parallel to each other. Todd Helmenstine

A parallelogram is a quadrangle where opposite sides are parallel to each other.
The perimeter (P) is the distance around the outside of the parallelogram.

P = 2a + 2b

The peak (h) is the perpendicular distance from one parallel side to its opposite side.​

Expanse = b x h

It is important to measure the correct side in this calculation. In the figure, the top is measured from side b to the contrary side b, so the expanse is calculated as b 10 h, not a x h. If the top was measured from a to a, then the area would be a x h. Convention calls the side the height is perpendicular to the "base." In formulas, the base of operations is usually denoted with a b.

Trapezoid Perimeter and Surface Area Formulas

A trapezoid is a quadrangle where only two opposing sides are parallel to each other. Todd Helmenstine

A trapezoid is another special quadrangle where only two sides are parallel to each other. The perpendicular distance between the two parallel sides is called the summit (h).

Perimeter = a + b_ane + b₂ + c

Expanse = ½( b_one + b_two ) x h

Circumvolve Perimeter and Surface Area Formulas

A circumvolve is a path where the distance from a center bespeak is abiding. Todd Helmenstine

A circle is an ellipse where the distance from the eye to the edge is constant.
Circumference (c) is the distance effectually the outside of the circle (its perimeter).
Diameter (d) is the distance of the line through the center of the circle from edge to edge. Radius (r) is the altitude from the center of the circumvolve to the edge.
The ratio betwixt the circumference and the diameter is equal to the number π.​

d = 2r

c = πd = 2πr

Area = πr²

Ellipse Perimeter and Surface Surface area Formulas

An ellipse is a effigy outlined past a path where the sum of the distances from two focal points are constant. Todd Helmenstine

An ellipse or oval is a figure that is traced out where the sum of the distances between 2 fixed points is a constant. The shortest distance betwixt the center of an ellipse to the edge is chosen the semiminor axis (r₁) The longest distance between the center of an ellipse to the border is called the semimajor axis (r₂).

Information technology's really rather hard to calculate the perimeter of an ellipse! The exact formula requires an infinite series, so approximations are used. One common approximation, which tin be used if r₂ is less than three times larger than r₁ (or the ellipse is not besides "squished") is:

Perimeter ≈ 2π [ (a² + b²) / two ]^½

Surface area = πr_aner_ii

Hexagon Perimeter and Surface Surface area Formulas

A regular hexagon is a half-dozen sided polygon where each side is of equal length. Todd Helmenstine

A regular hexagon is a six-sided polygon where each side is of equal length. This length is also equal to the radius (r) of the hexagon.

Perimeter = 6r

Area = (3√3/2 )r^two

Octagon Perimeter and Expanse Formulas

A regular octagon is a eight sided polygon where each side is of equal length. Todd Helmenstine

A regular octagon is an viii-sided polygon where each side is of equal length.

Perimeter = 8a

Expanse = ( 2 + 2√2 )a²

Watch Now: How to Calculate the Perimeter of a Triangle

Area Of Two Dimensional Shapes,

Source: https://www.thoughtco.com/perimeter-and-surface-area-formulas-604147

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