Surface Area of Triangular Pyramid Formula
The surface area of a triangular pyramid is the total area of all of the sides and faces of a triangular pyramid. Basically, A triangular pyramid has a triangular base and bounded by four triangular faces where 3 faces meet at one vertex. A triangular pyramid has all faces as triangles. This pyramid has 4 faces, 6 edges, and 4 corners. Few types of the triangular pyramid are given below:
Regular triangular pyramid, all faces are equilateral triangles and are known as tetrahedrons.
Right triangular pyramid, the base is an equilateral triangle while other faces are isosceles triangles.
An irregular triangular pyramid, a scalene, or isosceles triangle forms the base.
What Is Surface Area of A Right Triangular Pyramid
The surface area of any threedimensional geometrical shape is the sum of the areas of all of the faces or surfaces of that enclosed solid. A triangular pyramid has four triangular faces. Thus, The formula for calculating the surface area of a triangular pyramid involves the area of the base, the perimeter of the base, and the slant height of any side of the pyramid. The surface area of a triangular pyramid is \(\begin{align} \text {Base Area}+\!\frac{1}{2} \text {(Perimeter}\!\times\!\text {Slant Height}) \end{align}\). The surface area is always measured in square units like cm^{2}, m^{2}, ft^{2}, or cubits^{2}.
What Is the Surface Area of Triangular Pyramid Formula?
The Formula for the surface area of a triangular pyramid is calculated by adding up the area of all triangular faces of a pyramid. The surface area of a right triangular prism formula is \(\begin{align} \text {Base Area}+\!\frac{1}{2} \text {(Perimeter}\!\times\!\text {Slant Height}) \end{align}\). After putting the values we get an expression of the surface area of the triangular pyramid formula is 1⁄2(a × b) + 3⁄2(b × s)
Where 'b' is the side of the triangle pyramid.
'a' is the height of the base triangle
s is the slant height of a triangular prism.
'1⁄2(a × b)' is the base Area of the triangular faces.
3⁄2(b × s) is the product of the perimeter and slant height of a pyramid.
How to Calculate Surface Area of Triangular Pyramid
The surface area of a triangular pyramid can be calculated by representing the 3d figure into a 2d net, to make the shapes easier to see. After expanding the 3d figure into 2d we will get four triangles.
The following steps are used to calculate the surface area of a triangular pyramid:
 To find the area of the base triangles: The area of the base triangles is (1/2 × base of the triangle × height of the triangle) which becomes base × height.
 To find the perimeter of triangular faces: The perimeter of a triangle is the sum of all sides of a triangle which is side_{1}+side_{2}+side_{3}.
 To find the slant height of triangular faces: The slant height of a triangular pyramid is generally represented by 's'.
 Add all the areas together.
 Thus, the surface area of a triangular pyramid formula is 1⁄2(a × b) + 3⁄2(b × s) in squared units.
What Is the Lateral Surface Area of Triangular Pyramid
The lateral surface area is the area of the nonbase faces or we can say that only the lateral surface area of any object is calculated by removing the base area. The lateral area of a triangular pyramid can be calculated by removing a base area of a triangle with the product of the perimeter of the base and the slant height of a pyramid. Thus, the lateral surface area of a right triangular prism is "1⁄2(perimeter of the base × slant height)" which further becomes 3⁄2(side × slant height)
Where "b" is the side of a pyramid, and "s" is the slant height of the base.
Solved Examples on Surface Area of Triangular Pyramid Formula

Example 1
Each side of a triangular pyramid is of length 3 units, the height of the base triangle is 6, and the slant height is 5. Find its total surface area.
Solution
The surface area of a triangular pyramid of side \(a\) is
Surface Area= 1⁄2(a × b) + 3⁄2(b × s)
On Substituting the values, we get,
Surface Area=1⁄2(6 × 3) + 3⁄2(3 × 5)
Surface Area=(9) + (22.5)
Total Surface Area = 31.5units^{2}

Example 2
Find the surface area of a triangular pyramid whose area of the base triangles is 24 squared units, the perimeter of the triangle is 12 units, and the slant height of the pyramid is 18.
Solution
The area of the base triangles = 24 squared units.
The perimeter of the triangle =12 units.
The slant height of the pyramid =18 units.
The surface area of a triangular pyramid = \(\begin{align} \text {Base Area}+\!\frac{1}{2} \text {(Perimeter}\!\times\!\text {Slant Height}) \end{align}\)
Putting the values together,
The surface area of a triangular pyramid = \(\begin{align} \text {24}+\!\frac{1}{2} \text {(12}\!\times\!\text {18}) \end{align}\)
= 96 Squared Units.
Answer: The surface area of a triangular pyramid 96 Squared Units.
Practice Questions on Surface Area of Triangular Pyramid Formula
FAQs on Surface Area of Triangular Pyramid Formula
How Do You Find the Surface Area of a Triangular Pyramid?
The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. which is 1⁄2(a × b) + 3⁄2(b × s).
Where "b" is the side of a pyramid, "a" is the height of a base triangle, and "s" is the slant height of a pyramid.
What Is the Formula for the Volume and Surface Area of a Triangular Pyramid?
The volume of a triangular pyramid can be found by 1/3 × Base Area × Height.
How Do You Find the Area of the Base of a Right Triangular Pyramid?
The area of the base of a right triangular pyramid is 1/2 × height of a base triangle × the bottom edge of the base triangle.
What Is the Lateral Surface of a Triangular Pyramid?
The lateral surface of a triangular pyramid is calculated by multiplying 1/3 with the perimeter of the base triangle and the slant height a triangular pyramid.
What Is an Example of a Triangular Pyramid?
Camping tents, triangular roofs, and Toblerone warps chocolate are some common examples of a triangular pyramid.
How Many Edges Are in a Triangular Pyramid?
There are six edges in a right triangular prism.
What Is a Triangular Pyramid?
A triangular pyramid is a pyramid that has a triangular base and bounded by four triangular faces where 3 faces meet at one vertex.