| Area Formulas |
| (Math | Geometry | Area Formulas) |
(pi = = 3.141592..)
Area Formulas
Note: 'ab' means 'a' multiplied by 'b'. 'a2' means 'a squared', which is the same as 'a' times 'a'.
Be careful!! Units count. Use the same units for all measurements. Examples
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square = a 2
rectangle = ab
parallelogram = bh
trapezoid = h/2 (b1 + b2)
circle = pi r 2
ellipse = pi r1 r2
| triangle= | one half times the base length times the height of the triangle |
| equilateral triangle = |
triangle given SAS (two sides and the opposite angle)
= (1/2) a b sin C
triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula)
regular polygon = (1/2) n sin(360°/n) S2
when n = # of sides and S = length from center to a corner
Units
Area is measured in 'square' units. The area of a figure is the number of squares required to cover it completely, like tiles on a floor.
Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared.
If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches. (Square inches can also be written in2.)
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Be sure to use the same units for all measurements. You cannot multiply feet times inches, it doesn't make a square measurement.
The area of a rectangle is the length on the side times the width. If the width is 4 inches and the length is 6 feet, what is the area?
NOT CORRECT .. 4 times 6 = 24
CORRECT.. 4 inches is the same as 1/3 feet. Area is 1/3 feet times 6 feet = 2 square feet. (or 2 sq. ft., or 2 ft2).
Square Pyramid Shape
h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
Stot = total surface area
Slat = lateral surface area
Sbot = bottom surface area
Calculate more with
Pyramid Calculator
Calculator Use
Online calculator to calculate the surface area of geometric solids including a capsule, cone, frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere, spherical cap, and triangular prism
Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. For example, if you are starting with mm and you know r and h in mm, your calculations will result with V in mm3 and S in mm2.
Free movie editing for mac. Below are the standard formulas for surface area.
Surface Area Formulas:
Capsule Surface Area
- Volume = πr2((4/3)r + a)
- Surface Area = 2πr(2r + a)
Circular Cone Surface Area
- Volume = (1/3)πr2h
- Lateral Surface Area = πrs = πr√(r2 + h2)
- Base Surface Area = πr2
- Total Surface Area
= L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
Circular Cylinder Surface Area
Area Of A Trapezoid
- Volume = πr2h
- Top Surface Area = πr2
- Bottom Surface Area = πr2
- Total Surface Area
= L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Conical Frustum Surface Area
- Volume = (1/3)πh (r12 + r22 + (r1 * r2))
- Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2) - Top Surface Area = πr12
- Base Surface Area = πr22
- Total Surface Area
= π(r12 + r22 + (r1 * r2) * s)
= π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]
Cube Surface Area
- Volume = a3
- Surface Area = 6a2
Hemisphere Surface Area
- Volume = (2/3)πr3
- Curved Surface Area = 2πr2
- Base Surface Area = πr2
- Total Surface Area= (2πr2) + (πr2) = 3πr2
Pyramid Surface Area
- Volume = (1/3)a2h
- Lateral Surface Area = a√(a2 + 4h2)
- Base Surface Area = a2
- Total Surface Area
= L + B = a2 + a√(a2 + 4h2))
= a(a + √(a2 + 4h2))
Rectangular Prism Surface Area
- Volume = lwh
- Surface Area = 2(lw + lh + wh)
Sphere Surface Area
- Volume = (4/3)πr3
- Surface Area = 4πr2
Spherical Cap Surface Area
- Volume = (1/3)πh2(3R - h)
- Surface Area = 2πRh
Triangular Prism Surface Area
Top Surface Area of a Triangular Prism Formula
[ A_{top} = dfrac{1}{4} sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} ]Area Calculator
Bottom Surface Area of a Triangular Prism Formula
[ A_{bot} = dfrac{1}{4} sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} ]Lateral Surface Area of a Triangular Prism Formula
[ A_{lat} = h (a+b+c) ]Total Surface Area of a Triangular Prism Formula
[ A_{tot} = A_{top} + A_{bot} + A_{lat} ]Cite this content, page or calculator as:
Furey, Edward 'Surface Area Calculator'; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators