Triangular Prism Calculator

Get the useful formulas of a triangular prism in the following sections. You can check out the volume, total surface area, lateral surface area, top, and base surface area formulas on this page.

• Volume of a Triangular Prism Formula
  • V = ¼ h √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]
  • V = ½ * b * H * h
• Top Surface Area of a Triangular Prism Formula
  • Atop = ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]
  • Atop = ½ * b * H
• Bottom Surface Area of a Triangular Prism Formula
  • Abot = ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]
  • Abot = ½ * b * H
• Lateral Surface Area of a Triangular Prism Formula
  • Alat = h(a + b + c)
• Total Surface Area of a Triangular Prism Formula
  • Atot = Atop + Abot + Alat
• Height of a Triangular Prism Formula
  • h = (4V) / (√[(a + b +c )(b + c - a)(c + a - b)(a + b - c)])

Triangular Prism Calculations:

• If bottom triangle side, height, and prism height are given, then
  • Bottom triangle area Abot = ½ * b * H
  • Prism Volume V = Abot * h
• If triangle sides, lateral surface are being given, then
  • Prism height h = Alat / (a + b + c)
• If prism volume, height are given, then
  • Bottom surface area Abot = V / h

Where

a, b, c are the side lengths of a triangle

h is the triangular prism height

H is the height of the bottom triangle

V is the triangular prism volume

Atop is the top surface area of a triangular prism

Abot is the bottom surface area of a triangular prism

Alat is the lateral surface area of a triangular prism

Below given is the simple step-by-step process which is useful while solving the triangular prism unknown parameters. Use these easy steps to get the result quickly.

Triangular Prism Volume:

• Process 1:
  • Find out the triangle sides, and prism height
  • Divide the height by 4.
  • Add all sides of the triangle and add any two sides and subtract the third side from the sum.
  • Multiply the obtained 4 values.
  • Apply square root to the product.
  • Multiply the result with the value from step 2 to get the volume.
• Process 2:
  • Obtain the prism height, triangle base, height.
  • Multiply prism height, triangle height, and base.
  • Divide the product by 2 to check the volume.

Triangular Prism Top, Bottom Surface Area:

• Process 1:
  • Get three sides of the triangle from the question.
  • Add up all three side lengths.
  • And add two sides and subtract the third side from the sum repeat this process three times with three different sides.
  • Multiply the result from the above two steps.
  • Get the square root of the result and divide it by 4.
• Process 2:
  • Multiply the triangle base with height.
  • Divide the result by 2 to check the top, bottom surface areas.

Triangular Prism Lateral Surface Area:

• Note down the triangle sides and prism height.
• Add up three sides and multiply it with height to get the lateral surface area.

Triangular Prism Total Surface Area:

• The simple thing is add top, bottom, lateral surface areas of the triangular prism to get the result.

Triangular Prism Height:

• Process 1:
  • Observe the volume, sides of the triangle from the question.
  • Multiply the sum of 3 sides, sum two sides subtracted from the third side.
  • Apply square root to the product.
  • Divide 4 times of volume by the result to see prism height.
• Process 2:
  • Get the lateral surface area, triangle sides.
  • Divide the lateral surface area by the sum of three sides to check the height.

Example 1: Calculate the volume, surface area of a triangular prism with triangle height 4 cm, prism height 6 cm, and triangle base 4 cm?

Solution:

Given that,

Triangle height H = 4 cm

Prism height h = 6 cm

Trinagle base b = 4 cm

Triangular Prism Bottom Surface Area formula is Abot = ½ * b * H

= ½ * 4 * 4

= ½ * 16 = 8 cm²

Volume of a triangular prism formula is V = Abot * h

= 8 * 6

= 48 cm³

∴ Triangular Prism volume is 48 cm³, bottom surface area is 8 cm².

Example 2: Find the surface area, volume of a triangular prism having sides 16 m, 12 m, 20 m and height 29 m?

Solution:

Given that,

a = 16 m

b = 12 m

c = 20 m

Prism height h = 29 m

Triangular Prism Volume Formula is

V = ¼ h √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]

V = ¼ * 29 * √[(16 + 12 +20 )(12 + 20 - 16)(20 + 16 - 12)(16 + 12 - 20)]

= ¼ * 29 * √(48 * 16 * 24 * 8)

= ¼ * 29 * √147,456 = ¼ * 29 * 384

= ¼ * 11136 = 2,784 m³

Triangular Prism Top Surface Area Formula is

Atop = ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]

= ¼ * √[(16 + 12 +20 )(12 + 20 - 16)(20 + 16 - 12)(16 + 12 - 20)]

= ¼ * √(48 * 16 * 24 * 8)

= ¼ * √147,456

= ¼ * 384 = 96 m²

Triangular Prism Bottom Surface Area Formula is

Abot = ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]

= ¼ * √[(16 + 12 +20 )(12 + 20 - 16)(20 + 16 - 12)(16 + 12 - 20)]

= ¼ * √(48 * 16 * 24 * 8)

= ¼ * √147,456

= ¼ * 384 = 96 m²

Triangular Prism Lateral Surface Area Formula is

Alat = h(a + b + c)

= 29 * (16 + 12 +20)

= 29 * 48 = 1392 m²

Triangular Prism Total Surface Area Formula is

Atot = Atop + Abot + Alat

= 96 + 96 + 1392

= 1,584 m²

∴ Triangular Prism top, bottom surface areas are 96 m², lateral surface area is 1392 m², total surface area is 1,584 m², volume is 2,784 m³.

If you are looking for help while learning several geometry concepts then have a look at Areavolumecalculator.com for your queries and doubts all in one place .

1. What is the formula for the surface area of a triangular prism?

The general formulas to calculate the total surface area of a rectangular prism are one is perimeter * prism_height + base * traingle height. Other formula is calculate the top, bottom, and lateral surface areas and add those. Surface area is ½√[(a + b +c )(b + c - a)(c + a - b)(a + b - c)] + h(a + b + c).

2. How you find the missing length of a triangular prism?

The basic volume formula is ½ * length * width * height. So, check out the volume and other two parameters of the prism and substitute them in the formula to get the missing length easily.

3. What is the height of a triangular prism?

Height of the triangular prism is the length of the line that joins bottom, top triangles. Simple formulas to calculate the height are lateral_surface_area / perimeter, (4 * volume) / (√[(a + b +c )(b + c - a)(c + a - b)(a + b - c)]), Volume / bottom_surfcae area.

4. What are the properties of a triangular prism?

It has 9 edges, 5 faces, and 6 vertices.

It has three triangular bases and three rectangular sides.