https://file.aiquickdraw.com/mathbot/file/1726308877549ooeibr2g.jpg

The given shape appears to be a triangular prism. To calculate the surface area of this shape, we need to sum the areas of all the faces of the prism.

The triangular prism consists of:
1. Two triangular faces
2. Three rectangular faces

### Step 1: Calculate the area of the triangular faces
Each triangular face has a base of 7.2 cm and a height of 3.5 cm (as indicated in the diagram).

The area of a triangle is given by:

\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the values:

\[
A_{\text{triangle}} = \frac{1}{2} \times 7.2 \, \text{cm} \times 3.5 \, \text{cm} = 12.6 \, \text{cm}^2
\]

So, the area of one triangular face is \(12.6 \, \text{cm}^2\), and since there are two triangular faces, the total area for both triangles is:

\[
\text{Total triangle area} = 2 \times 12.6 = 25.2 \, \text{cm}^2
\]

### Step 2: Calculate the area of the rectangular faces
There are three rectangular faces, and their areas can be calculated as follows:

1. **Front face (base × height):** 
   The front face is a rectangle with dimensions 8 cm × 5 cm.

   \[
   A_{\text{front}} = 8 \, \text{cm} \times 5 \, \text{cm} = 40 \, \text{cm}^2
   \]

2. **Bottom face (base × side length):**
   The bottom face is a rectangle with dimensions 8 cm × 7.2 cm.

   \[
   A_{\text{bottom}} = 8 \, \text{cm} \times 7.2 \, \text{cm} = 57.6 \, \text{cm}^2
   \]

3. **Slant face (slant height × side length):**
   The slant face is a rectangle with dimensions 8 cm × 5 cm (slant height).

   \[
   A_{\text{slant}} = 8 \, \text{cm} \times 5 \, \text{cm} = 40 \, \text{cm}^2
   \]

### Step 3: Add up the areas of all faces
Now, summing the areas of all the faces:

\[
\text{Total surface area} = (\text{Total triangle area}) + A_{\text{front}} + A_{\text{bottom}} + A_{\text{slant}}
\]
\[
\text{Total surface area} = 25.2 \, \text{cm}^2 + 40 \, \text{cm}^2 + 57.6 \, \text{cm}^2 + 40 \, \text{cm}^2 = 162.8 \, \text{cm}^2
\]

Thus, the total surface area of the prism is **162.8 cm²**.

Do you want any details or have any questions?

Here are five related questions to expand your understanding:
1. How would the surface area change if the height of the triangle doubled?
2. Can you calculate the volume of this triangular prism using the given dimensions?
3. What formula would you use to find the surface area if the base was a different polygon?
4. How does the slant height of the triangle affect the overall surface area?
5. Can you explain how surface area differs from lateral surface area in a prism?

**Tip:** When calculating the surface area of a 3D shape, always ensure you account for every face, especially if the shape is irregular.

Learn how to calculate the surface area of a triangular prism with base 7.2 cm, height 3.5 cm, and rectangular faces. This geometry problem walks through each step, applying formulas for the area of triangles and rectangles. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation