# Triangular Prism Calculator

Triangular Prism is a prism with two triangular bases and three edges. The sides of the prism are in a rectangular shape and edges join the corresponding sides. Two base triangles are equilateral triangles and edges are parallel to each other.

** Triangular Prism Calculator: **If you are in search of a free online tool that calculates the triangular prism height, sides, volume, and surface area fastly you have arrived the right way. Take the help of the user-friendly tool provided here and evaluate the unknown measures in no time. Furthermore, we have given the formulas, step by step procedure to find the measurements of a triangular prism. Have a glance at the best solved examples for a better understanding of the concept.

Utilize the Triangular Prism Calculator to compute the height, volume, and surface area. Simply input the known parameters and tap on the calculate button to get the result in a blink of an eye.

## The Formulas of Triangular Prism

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**- A
_{top}= ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)] - A
_{top}= ½ * b * H **Bottom Surface Area of a Triangular Prism Formula**- A
_{bot}= ¼ √[(a + b +c )(b + c - a)(c + a - b)(a + b - c)] - A
_{bot}= ½ * b * H **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} **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 A
_{bot}= ½ * b * H - Prism Volume V = A
_{bot}* h - If triangle sides, lateral surface are being given, then
- Prism height h = A
_{lat}/ (a + b + c) - If prism volume, height are given, then
- Bottom surface area A
_{bot}= 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

A_{top} is the top surface area of a triangular prism

A_{bot} is the bottom surface area of a triangular prism

A_{lat} is the lateral surface area of a triangular prism

### Steps to Find Triangular Prism volume, Area

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 Questions

**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 A_{bot} = ½ * b * H

= ½ * 4 * 4

= ½ * 16 = 8 cm²

Volume of a triangular prism formula is V = A_{bot} * 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

A_{top} = 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

A_{bot} = 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

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

= 29 * (16 + 12 +20)

= 29 * 48 = 1392 m²

Triangular Prism Total Surface Area Formula is

A_{tot} = A_{top} + A_{bot} + A_{lat}

= 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.

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### FAQs on Triangular Prism

**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.