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2 <p>Last updated on<strong>September 4, 2025</strong></p>

3 <p>A triangular prism is a three-dimensional shape that has two identical triangular bases and three rectangular faces. The surface area of a triangular prism is the total area covered by its outer surface. This includes the areas of the two triangular bases and the three rectangular sides. In this article, we will learn about the surface area of a triangular prism.</p>

4 <h2>What is the Surface Area of a Triangular Prism?</h2>

5 <p>The surface area of a triangular prism is the total area occupied by the boundary or outer surface of the prism.It is measured in<a>square</a>units.</p>

6 <p>A triangular prism has two parallel triangular bases and three rectangular lateral surfaces.</p>

7 <p>Therefore, the surface area includes the areas of the two triangular bases and the three rectangles.</p>

8 <p>Triangular prisms can be right or oblique.A right triangular prism has rectangular lateral surfaces perpendicular to its bases, while an oblique triangular prism has lateral surfaces that are not perpendicular.</p>

9 <h2>Surface Area of a Triangular Prism Formula</h2>

10 <p>A triangular prism has two types of surface areas: the lateral surface area and the total surface area.Look at the triangular prism below to see its surface area,<a>base</a>area, and height.</p>

11 <p>A triangular prism has two types of surface areas:</p>

12 <ol><li>Lateral Surface Area of a Triangular Prism</li>

13 <li>Total Surface Area of a Triangular Prism</li>

14 </ol><h2>Lateral Surface Area of a Triangular Prism</h2>

15 <p>The lateral surface area of a triangular prism is the<a>sum</a>of the areas of its three rectangular sides.It does not include the area of the bases.</p>

16 <p>The<a>formula</a>for the LSA (Lateral Surface Area) of the triangular prism is given as:</p>

17 <p>Lateral Surface Area = perimeter of base × height</p>

18 <p>Here, the perimeter of the base is the sum of the sides of the triangular base.</p>

19 <p>The height is the perpendicular distance between the two triangular bases.</p>

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22 <h2>Total Surface Area of a Triangular Prism</h2>

21 <h2>Total Surface Area of a Triangular Prism</h2>

23 <p>The total surface area of a triangular prism is the sum of the lateral surface area and the area of the two triangular bases. The formula for the total surface area is:</p>

22 <p>The total surface area of a triangular prism is the sum of the lateral surface area and the area of the two triangular bases. The formula for the total surface area is:</p>

24 <p>Total Surface Area = Lateral Surface Area + 2 × Base Area</p>

23 <p>Total Surface Area = Lateral Surface Area + 2 × Base Area</p>

25 <p>Where the Base Area is the area of one triangular base.</p>

24 <p>Where the Base Area is the area of one triangular base.</p>

26 <p>Derivation of the Total Surface Area of a Triangular Prism</p>

25 <p>Derivation of the Total Surface Area of a Triangular Prism</p>

27 <p>To find the total surface area, add the lateral area and twice the area of the base.</p>

26 <p>To find the total surface area, add the lateral area and twice the area of the base.</p>

28 <p>Consider a triangular prism with base area (B), height (h), and base perimeter (P).</p>

27 <p>Consider a triangular prism with base area (B), height (h), and base perimeter (P).</p>

29 <p>Total surface area of a triangular prism = 2 × Base Area + Lateral Surface Area</p>

28 <p>Total surface area of a triangular prism = 2 × Base Area + Lateral Surface Area</p>

30 <p>Here, Base Area = area of one triangular base</p>

29 <p>Here, Base Area = area of one triangular base</p>

31 <p>Lateral Surface Area = perimeter of base × height</p>

30 <p>Lateral Surface Area = perimeter of base × height</p>

32 <h2>Volume of a Triangular Prism</h2>

31 <h2>Volume of a Triangular Prism</h2>

33 <p>The volume of a triangular prism shows how much space is inside it. It tells us the capacity of the prism.</p>

32 <p>The volume of a triangular prism shows how much space is inside it. It tells us the capacity of the prism.</p>

34 <p>The volume can be found using the formula: Volume = Base Area × height (cubic units)</p>

33 <p>The volume can be found using the formula: Volume = Base Area × height (cubic units)</p>

35 <h2>Confusion between LSA and TSA</h2>

34 <h2>Confusion between LSA and TSA</h2>

36 <p>Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a triangular prism are the same. Remember, LSA only includes the rectangular sides, while TSA includes both the lateral surface and the bases.</p>

35 <p>Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a triangular prism are the same. Remember, LSA only includes the rectangular sides, while TSA includes both the lateral surface and the bases.</p>

37 <h3>Problem 1</h3>

36 <h3>Problem 1</h3>

38 <p>Given P = 12 cm, h = 5 cm. Use the formula: LSA = perimeter of base × height = 12 × 5 = 60 cm²</p>

37 <p>Given P = 12 cm, h = 5 cm. Use the formula: LSA = perimeter of base × height = 12 × 5 = 60 cm²</p>

39 <p>Okay, lets begin</p>

38 <p>Okay, lets begin</p>

40 <p>Find the total surface area of a triangular prism with base area of 10 cm², base perimeter of 14 cm, and height of 6 cm.</p>

39 <p>Find the total surface area of a triangular prism with base area of 10 cm², base perimeter of 14 cm, and height of 6 cm.</p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>TSA = 104 cm²</p>

41 <p>TSA = 104 cm²</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>Use the formula: TSA = 2 × Base Area + Lateral Surface Area = 2 × 10 + (14 × 6) = 20 + 84 = 104 cm²</p>

44 <p>Use the formula: TSA = 2 × Base Area + Lateral Surface Area = 2 × 10 + (14 × 6) = 20 + 84 = 104 cm²</p>

46 <p>Okay, lets begin</p>

45 <p>Okay, lets begin</p>

47 <p>A triangular prism has a base area of 15 cm², a base perimeter of 18 cm, and a height of 7 cm.</p>

46 <p>A triangular prism has a base area of 15 cm², a base perimeter of 18 cm, and a height of 7 cm.</p>

48 <p>Find the total surface area.</p>

47 <p>Find the total surface area.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>TSA = 156 cm²</p>

49 <p>TSA = 156 cm²</p>

51 <p>Well explained 👍</p>

50 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

51 <h3>Problem 3</h3>

53 <p>Use the TSA formula: TSA = 2 × Base Area + Lateral Surface Area = 2 × 15 + (18 × 7) = 30 + 126 = 156 cm²</p>

52 <p>Use the TSA formula: TSA = 2 × Base Area + Lateral Surface Area = 2 × 15 + (18 × 7) = 30 + 126 = 156 cm²</p>

54 <p>Okay, lets begin</p>

53 <p>Okay, lets begin</p>

55 <p>Find the lateral surface area of a triangular prism with a base perimeter of 20 cm and height of 8 cm.</p>

54 <p>Find the lateral surface area of a triangular prism with a base perimeter of 20 cm and height of 8 cm.</p>

56 <h3>Explanation</h3>

55 <h3>Explanation</h3>

57 <p>LSA = 160 cm²</p>

56 <p>LSA = 160 cm²</p>

58 <p>Well explained 👍</p>

57 <p>Well explained 👍</p>

59 <h3>Problem 4</h3>

58 <h3>Problem 4</h3>

60 <p>LSA = perimeter of base × height = 20 × 8 = 160 cm²</p>

59 <p>LSA = perimeter of base × height = 20 × 8 = 160 cm²</p>

61 <p>Okay, lets begin</p>

60 <p>Okay, lets begin</p>

62 <p>The height of a triangular prism is 10 cm, and its lateral surface area is 200 cm².</p>

61 <p>The height of a triangular prism is 10 cm, and its lateral surface area is 200 cm².</p>

63 <p>Find the base perimeter.</p>

62 <p>Find the base perimeter.</p>

64 <h3>Explanation</h3>

63 <h3>Explanation</h3>

65 <p>Base perimeter = 20 cm</p>

64 <p>Base perimeter = 20 cm</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h2>It is the total area that covers the outside of the prism, including its lateral surface and the bases.</h2>

66 <h2>It is the total area that covers the outside of the prism, including its lateral surface and the bases.</h2>

68 <h3>1.What are the two types of surface area in a triangular prism?</h3>

67 <h3>1.What are the two types of surface area in a triangular prism?</h3>

69 <p>Lateral surface area and total surface area are the two types of surface area in a triangular prism.</p>

68 <p>Lateral surface area and total surface area are the two types of surface area in a triangular prism.</p>

70 <h3>2.How do you find the height of a triangular base?</h3>

69 <h3>2.How do you find the height of a triangular base?</h3>

71 <p>The height of the triangular base is the perpendicular distance from a vertex to the opposite side or base of the triangle.</p>

70 <p>The height of the triangular base is the perpendicular distance from a vertex to the opposite side or base of the triangle.</p>

72 <h3>3.Is lateral surface area the same as total surface area?</h3>

71 <h3>3.Is lateral surface area the same as total surface area?</h3>

73 <p>No, the lateral surface area does not include the bases, while the total surface area includes both the lateral surface and the bases.</p>

72 <p>No, the lateral surface area does not include the bases, while the total surface area includes both the lateral surface and the bases.</p>

74 <h3>4.What unit is surface area measured in?</h3>

73 <h3>4.What unit is surface area measured in?</h3>

75 <p>Surface area is always measured in square units like cm², m², or in².</p>

74 <p>Surface area is always measured in square units like cm², m², or in².</p>

76 <h2>Common Mistakes and How to Avoid Them in the Surface Area of a Triangular Prism</h2>

75 <h2>Common Mistakes and How to Avoid Them in the Surface Area of a Triangular Prism</h2>

77 <p>Students often make mistakes while calculating the surface area of a triangular prism, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.</p>

76 <p>Students often make mistakes while calculating the surface area of a triangular prism, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.</p>

78 <p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

77 <p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

79 <p>▶</p>

78 <p>▶</p>

80 <h2>Seyed Ali Fathima S</h2>

79 <h2>Seyed Ali Fathima S</h2>

81 <h3>About the Author</h3>

80 <h3>About the Author</h3>

82 <p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>

81 <p>Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.</p>

83 <h3>Fun Fact</h3>

82 <h3>Fun Fact</h3>

84 <p>: She has songs for each table which helps her to remember the tables</p>

83 <p>: She has songs for each table which helps her to remember the tables</p>