Volume Of A Triangular Pyramid

Triangular Pyramid Formula

A triangular pyramid has a triangle-shaped base of operations and all 3 triangular faces meet at the apex. There is a special case of a triangular pyramid called a tetrahedron, it has equilateral triangles for each of the faces. The triangular pyramid formula consists of both the volume and the surface area of the triangular pyramid that calculates the three triangular-shaped sides, the elevation, and the slant peak. The following effigy shows how a triangular pyramid looks like:

Triangular Pyramid with height and slant height

What is Triangular Pyramid Formula?

A pyramid with a triangle-shaped base whose three triangular faces come across at the noon. The triangular pyramid formula included both the volume and surface surface area of the pyramid. The triangular pyramid book formula calculates the base of operations expanse and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter, and slant meridian. Formulas for volume and surface surface area of the triangular pyramid are given below that are used in the triangular pyramid formula:

Volume= 1/iii × Base of operations area ×Height

Surface Surface area = Base of operations expanse +1/two(perimeter × slant height)

Triangular Pyramid Formula

Formulas for volume and surface area of the triangular pyramid are:

Volume= 1/3 × Base area ×Top

Surface Area = Base of operations area +ane/2(perimeter × slant height)

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Examples Using Triangular Pyramid Formula

Example 1: Detect the volume of a triangular pyramid having a base area of 10 cm² and a height of 5 cm.

Solution:

Given: base area = ten cmⁱⁱ, height = 5 cm.

Using the formula for the volume of a triangular pyramid

Volume =1/three × Base area × Acme

= 1/3 × 10 × five

= 16.67 cmⁱⁱⁱ

Therefore, the volume of the triangular pyramid is sixteen.67 cm^three

Instance 2: A triangular pyramid has a base of operations area of fifteen units^two and a sum of the lengths of the edges 60 units. Calculate the surface area of the triangular pyramid if the camber tiptop is xx units.

Solution:
Given: Base area =15 units², perimeter = sixty units.

Using the formula for surface area of triangular pyramid

Surface Area = Base surface area + 1/2(perimeter × slant height)

= 15 + 1/2(lx × xx)
= 15 + 600
= 615 unit²

Therefore, the surface area of the triangular pyramid is 615 unit of measurement²

Example 3: Find the expanse of a triangular pyramid whose area of the base triangles is 24 square units, the perimeter of the triangle is 12 units, and the camber height of the pyramid is xviii.

Solution:

The surface area of the base triangles = 24 squared units.

The perimeter of the triangle =12 units.

The slant acme of the pyramid =18 units.

Using the formula for the surface area of a triangular pyramid

The surface surface area of a triangular pyramid = Base of operations Area+ 1/ii(Perimeter × Camber Superlative)

= 24 + 1/ii (12 × 18)

= 132 unit ²

Therefore, the surface area of a triangular pyramid 132 unit^two

FAQs on Triangular Pyramid Formula

What is Meant by Triangular Pyramid Formula?

A triangular pyramid has a triangle-shaped base and all iii triangular faces see at the apex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid book formula calculates the base area and the acme whereas the surface area of the triangular pyramid calculates the base of operations surface area, perimeter, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula:

Volume= 1/iii × Base of operations expanse × Height

Surface Area = Base surface area +1/ii(perimeter × slant height)

How Do Yous Find the Surface Area of a Triangular Pyramid?

The formula for the surface area of a pyramid is calculated by calculation up the area of all triangular faces of a pyramid. which is Base of operations area +one/two(perimeter × slant summit). The dimensions required to observe the surface surface area of a triangular pyramid are the side, height, and slant acme.

How Do You Find the Book of a Triangular Pyramid?

The formula for calculating the volume of a triangular pyramid is Volume= one/iii × Base area × Height. The dimensions required to find the surface area of a triangular pyramid are the side, height, and slant top.

Using the Triangular Pyramid Formula, Detect the Volume with a Base Area of 15 cm² and a height of iv cm.

Given: base area = 15 cm^two, meridian = four cm.

Using the formula for the volume of a triangular pyramid

Volume =1/3 × Base surface area × Meridian

= 1/3 × xv × 4

= xx cm^three

Therefore, the volume of the triangular pyramid is twenty cm³