Surface Area of A Right Triangular Prism
The surface area of a right triangular prism is the total area of all of the sides and faces of a right triangular prism. Basically, a right triangular prism is a prism that has two parallel and congruent triangular faces and three rectangular faces perpendicular to the triangular faces. In this lesson, we will learn to determine the surface area of a right triangular prism.
What is Surface Area of a Right Triangular Prism?
The surface area of a right triangular prism is the sum of the areas of all of the faces or surfaces of the prism. A right triangular prism has three rectangular sides and two right triangular faces. In a right triangular prism, the rectangular faces are said to be lateral, while the triangular faces are called bases. If the bases of a right triangular prism are kept horizontal, they are sometimes called the top and the bottom (faces) of a right triangular prism. This prism has 6 vertices, 9 edges, and 5 faces. There are two types of surface areas in the case of the surface area of a right triangular prism:
 Lateral surface area
 Total surface area
The unit of the surface area of a right triangular prism is expressed in square units, m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
Formula of Surface Area of a Right Triangular Prism
The formula for the surface area of a right triangular prism is calculated by adding up the area of all rectangular and triangular faces of a prism. The surface area of a right triangular prism formula is Surface area = (Length × Perimeter) + (2 × Base Area) = (\(s_{1}\)_{ }+ \(s_{2}\) + h)L + bh where "b" is the bottom edge of the base triangle, "h" is the height of the base triangle, "L" is the length of the prism and \(s_{1}\), \(s_{2}\) are the two edges of the base triangle. "bh" is the combined area of two triangular faces. The (s_{1 }+ s_{2} +h)L is the area of the three rectangular side faces. The surface area of a right triangular prism is also referred to as its total surface area.
The lateral surface area of any object is calculated by removing the base area or we can say that the lateral surface area is the area of the nonbase faces only. When the right triangular prism has its bases facing up and down, the lateral area is the area of the vertical faces. The lateral area of a right triangular prism can be calculated by multiplying the perimeter of the base by the length of the prism. Thus, the lateral surface area of a right triangular prism is "l × p" where "l" is the height of a prism, and "p" is the perimeter of the base which is given as LSA = (\(s_{1}\)_{ }+ \(s_{2}\) + h)L = (Length × Perimeter).
How to Calculate Surface Area of a Right Triangular Prism?
The surface area of a right triangular prism can be calculated by representing the 3d figure into a 2d net, to make the shapes easier to see. After expanding this 3d shape into the 2d shape we will get two right triangles and three rectangles. The following steps are used to calculate the surface area of a right triangular prism :
 Step 1: Find the area of the top and the base triangles using the formula 2 ×(1/2 × base of the triangle × height of the triangle) which becomes base × height.
 Step 2: Find the product of the length of the prism to the perimeter of the base triangle.
 Step 3: Add all the areas together.
 Step 4: Thus, the surface area of a right triangular prism is written in squared units.
Example: Find the surface area of a right triangular prism, having a base area of 60 square units, the base perimeter of 40 units, and the length of the prism of 7 units.
Solution: Given base area = 60 square units, p = 40 units and length of prism = 7 units
Thus, the surface area of the right triangular prism, S = (Length × Perimeter) + (2 × Base Area)
⇒ S = (7 × 40) + (2 × 60)
⇒ S = (280 + 120) square units
⇒ S = 400 square units
Thus, the surface area of the right triangular prism is 400 square units
Solved Examples on Surface Area of a Right Triangular Prism

Example 1: Find the surface area of the right triangular prism shown below.
Solution: Given b = 5 units, the height of the triangle (h) = 12 units, length of a prism = 11, and the hypotenuse of a right triangle =13.
The surface area of a right triangular prism is bh+(s_{1 }+ s_{2} + h)L
On putting the values, we get
SA = 5 × 12 + (5 + 13+ 12) × 11
⇒ SA = 60 + (30) ×11
⇒ SA = 390 squared units.Answer: The surface area of a right triangular prism is 390 squared units.

Example 2: Find the surface area of a right triangular prism whose area of the top and base triangles is 30 squared units each, the perimeter of the right triangle is 11 units, and the length of the prism is 25 units.
Solution: Given area of top and base triangles = 30 squared units, the perimeter of the right triangle = 11 units, and length of triangle = 25 units
The combined area of the top and base triangles = (30+30) = 60 squared units.
The perimeter of the right triangle =11 units.
The length of the prism = 25 units.The surface area of a right triangular prism = The combined area of the top and base triangles + (The perimeter of the right triangle) × The length of the prism.
Putting the values together,
The surface area of a right triangular prism = 60 + (11 × 25) = 335 square unitsAnswer: The surface area of a right triangular prism 335 square units.
Practice Questions on Surface Area of a Right Triangular Prism
FAQs on Surface Area of a Right Triangular Prism
What is the Surface Area of a Right Triangular Prism?
The surface area of a right triangular prism is defined as the sum of the areas of all of the faces or surfaces of the prism. We can find the total surface area and lateral surface area in the case of a right triangular prism.
What is the Formula of Surface Area of a Right Triangular Prism?
The formula of the surface area of a right triangular prism is (Length × Perimeter) + (2 × Base Area) = (\(s_{1}\)_{ }+ \(s_{2}\) + h)L + bh where "b" is the bottom edge of the base triangle, "h" is the height of the base triangle, "L" is the length of the prism and \(s_{1}\), \(s_{2}\) are the two edges of the base triangle.
What is the Unit of Surface Area of a Right Triangular Prism?
The unit of the surface area of a right triangular prism is given in square units, for example, m^{2}, cm^{2}, in^{2} or ft^{2}, etc.
How to Find the Surface Area of a Right Triangular Prism?
We use the following steps to calculate the surface area of a right triangular prism :
 Step 1: Determine the area of the top and the base triangles using the formula 2 ×(1/2 × base of the triangle × height of the triangle) which becomes base × height.
 Step 2: Determine the product of the length of the prism to the perimeter of the base triangle.
 Step 3: Now, add all the areas together.
 Step 4: The surface area of a right triangular prism is written in squared units.
How to Find the Lateral Surface Area of a Right Triangular Prism?
We use the following steps to calculate the lateral surface area of a right triangular prism :
 Step 1: Identify the length of the prism from the given dimensions.
 Step 2: Find the perimeter of the base of the prism.
 Step 3: Now, multiply them.
 Step 4: The lateral surface area of a right triangular prism is expressed in squared units.
How to Find the Base Area If the Surface Area of a Right Triangular Prism is Given?
We use the following steps to calculate the base area if the surface area of a right triangular prism is given:
 Step 1: Identify the given dimensions.
 Step 2: Now use the formula (Length × Perimeter) + (2 × Base Area) and assume the base area is "b"
 Step 3: Now, substitute the values and solve for "b".
 Step 4: The obtained value of "b" is written in units.
What Happens to the Surface Area of a Right Triangular Prism If the Length of Prism Is Doubled?
The surface area of the right triangular prism increases in magnitude when the length of the prism is doubled. However, the surface area of the right triangular prism does not double as the surface area of the right triangular prism does not depend entirely on the length of the prism.