Solved Examples: Surface Area of Triangular Prisms

📚 Quick Study Guide

• 📐 Definition: A triangular prism is a 3D shape with two triangular bases and three rectangular sides.
• 📏 Surface Area Formula: The surface area (SA) is the sum of the areas of all its faces. For a triangular prism, this is: $SA = 2 * (Area \, of \, Triangle) + (Area \, of \, Rectangle_1) + (Area \, of \, Rectangle_2) + (Area \, of \, Rectangle_3)$
• 🔎 Area of a Triangle: The area of a triangle is given by $Area = \frac{1}{2} * base * height$.
• ✨ Area of a Rectangle: The area of a rectangle is given by $Area = length * width$.
• 🔢 Simplified Formula: If 'b' is the base of the triangle, 'h' is the height of the triangle, and $l_1$, $l_2$, $l_3$ are the lengths of the three sides of the rectangular faces, and 'L' is the length of the prism, then: $SA = (b*h) + (l_1*L) + (l_2*L) + (l_3*L)$

🧪 Practice Quiz

1. What is the surface area of a triangular prism with a base triangle having a base of 6 cm, a height of 4 cm, a prism length of 10 cm, and rectangle side lengths of 5 cm, 6 cm, and 5 cm?

   1. 168 cm²
   2. 180 cm²
   3. 192 cm²
   4. 204 cm²

2. A triangular prism has a base triangle with an area of 20 cm². The three rectangular faces have areas of 50 cm², 60 cm², and 70 cm². What is the total surface area of the prism?

   1. 180 cm²
   2. 200 cm²
   3. 220 cm²
   4. 240 cm²

3. Calculate the surface area of a triangular prism where the base triangle has a base of 8 cm and a height of 5 cm. The prism's length is 12 cm, and the rectangle side lengths are 7 cm, 8 cm, and 7 cm.

   1. 288 cm²
   2. 300 cm²
   3. 320 cm²
   4. 336 cm²

4. A triangular prism has an equilateral triangle as its base, with each side measuring 4 cm. The height of this triangle is approximately 3.46 cm. The length of the prism is 8 cm. What is the surface area, given the rectangular faces are equal?

   1. 115.04 cm²
   2. 120.04 cm²
   3. 125.04 cm²
   4. 130.04 cm²

5. What is the surface area of a triangular prism if the area of one triangular base is 25 cm², and the areas of the three rectangular faces are 75 cm², 80 cm², and 85 cm²?

   1. 240 cm²
   2. 265 cm²
   3. 290 cm²
   4. 315 cm²

6. Find the surface area of a triangular prism with a right-angled triangle base. The sides of the triangle are 3 cm, 4 cm, and 5 cm (hypotenuse). The length of the prism is 9 cm.

   1. 150 cm²
   2. 156 cm²
   3. 162 cm²
   4. 168 cm²

7. A triangular prism has a surface area of 360 cm². If the combined area of the three rectangular faces is 270 cm², what is the area of each triangular base?

   1. 35 cm²
   2. 40 cm²
   3. 45 cm²
   4. 50 cm²