how do you find the surface area

Foursquare Pyramid Shape

h = height
s = slant height
a = side length
e = lateral border length
r = a/2
Five = volume
S_tot = full surface area
Due south_lat = lateral surface area
S_bot = bottom surface area

Calculate more with
Pyramid Calculator

Computer Use

Online calculator to calculate the 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 practise not touch on the calculations. The units are in place to requite an indication of the order of the results such equally ft, ft² or ft³. For example, if you lot are starting with mm and yous know r and h in mm, your calculations will result with Five in mmⁱⁱⁱ and S in mm².

Below are the standard formulas for surface surface area.

Surface Area Formulas:

Capsule Surface Surface area

• Volume = πrⁱⁱ((iv/3)r + a)
• Area = 2πr(2r + a)

Round Cone Expanse

• Book = (1/3)πr^twoh
• Lateral Surface Expanse = πrs = πr√(r^two + h²)
• Base Surface Surface area = πr²
• Full Surface Area
  = Fifty + B = πrs + πr² = πr(s + r) = πr(r + √(r² + h²))

Circular Cylinder Surface Area

• Volume = πr²h
• Top Surface Area = πr²
• Bottom Surface Area = πrⁱⁱ
• Total Surface Expanse
  = L + T + B = 2πrh + ii(πr^two) = 2πr(h+r)

Conical Frustum Area

• Volume = (1/3)πh (r_ane ⁱⁱ + r_ii ² + (r₁ * r_ii))
• Lateral Expanse
  = π(r_one + r_two)s = π(r₁ + r₂)√((r₁ - r_ii)² + h²)
• Tiptop Expanse = πr₁ ²
• Base Surface Surface area = πr_two ²
• Total Surface Area
  = π(r₁ ² + r₂ ² + (r₁ * r₂) * s)
  = π[ r₁ ² + r_ii ² + (r₁ * r_two) * √((r₁ - r₂)² + h²) ]

Cube Expanse

• Volume = a³
• Area = 6a²

Hemisphere Surface Area

• Volume = (two/3)πrⁱⁱⁱ
• Curved Surface Area = iiπr²
• Base Surface Area = πrⁱⁱ
• Full Area= (2πrⁱⁱ) + (πr²) = iiiπrⁱⁱ

Pyramid Surface Expanse

• Volume = (1/3)aⁱⁱh
• Lateral Surface Surface area = a√(aⁱⁱ + 4h²)
• Base Surface Expanse = a^two
• Total Surface Area
  = L + B = aⁱⁱ + a√(a² + 4h²))
  = a(a + √(a^two + 4h²))

Rectangular Prism Surface Area

• Book = lwh
• Area = 2(lw + lh + wh)

Sphere Surface Expanse

• Book = (4/three)πr³
• Area = 4πr²

Spherical Cap Expanse

• Book = (ane/three)πh²(3R - h)
• Surface Area = 2πRh

Triangular Prism Surface Expanse

Top Surface Surface area of a Triangular Prism Formula

\[ A_{tiptop} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

\[ A_{elevation} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\finish{aligned}} \]

Bottom Surface Area of a Triangular Prism Formula

\[ A_{bot} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

\[ A_{bot} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]

Lateral Expanse of a Triangular Prism Formula

\[ A_{lat} = h (a+b+c) \]

Total Surface area of a Triangular Prism Formula

\[ A_{tot} = A_{top} + A_{bot} + A_{lat} \]

Source: https://www.calculatorsoup.com/calculators/geometry-solids/surfacearea.php

Posted by: losoyawhavuld.blogspot.com

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