Triangular Pyramid Calculator

Triangular Pyramid Calculator is a free online tool that displays the surface area and the volume of the triangular pyramid. BYJU’S online triangular pyramid calculator tool performs the calculation faster and it displays the surface area and volume in a fraction of seconds.

How to Use the Triangular Pyramid Calculator? 

The procedure to use the triangular pyramid calculator is as follows:

Step 1: Enter the side length, height, slant height, and apothem length of the triangular pyramid in the input field

Step 2: Now click the button “Calculate” to get the surface area and volume

Step 3: Finally, the surface area and the volume of a triangular pyramid will be displayed in the output field

What is Meant by the Triangular Pyramid?

In geometry, a pyramid is defined as the three-dimensional figure with a triangular or square base, and faces of the pyramid meet at a common point called the apex. Based on the base of the pyramid, the pyramid can be classified into different types, such as the triangular pyramid, square pyramid, right pyramid, oblique pyramid and so on. A triangular pyramid is a pyramid, whose base and the faces of the pyramid are triangles. The formula to calculate the surface area and the volume of a triangular pyramid is given as:

The surface area of a triangular pyramid = Base area + [(3/2) × slant height × base length)] square units

The volume of a triangular pyramid, V = (⅓) × Base area × Height cubic units

Solved Example on Triangular Pyramid

Example 1:

Find the surface area and the volume of a triangular Pyramid whose side length is 4 cm, apothem length is 5 cm, slant height is 7 cm, and height is 6 cm.

Solution:

Given that, 

Side length = 4cm

Apothem length = 5 cm

Slant height =  7 cm

Height = 6 cm

Now substitute the values in the formula, we get

The surface area of a triangular pyramid = Base area + [(3/2) × slant height × base length)] square units

Base Area = (½)(4×5)

Base area = 20/2

Base area = 10 cm².

Therefore, SA = 10 + [(3/2)(7)(4)]

SA = 10+ 14(3)

SA =10 + 42

SA = 52 cm².

The volume of a triangular pyramid, V = (⅓) × Base area × Height cubic units

V = (⅓)  × 10 × 6

V = 10  × 2

V = 20 cm³.