Question

What is the surface area of the triangular prism dimensions 8 cm 6 cm 9 cm 10 cm base 5 height 4 inches

Answer 1

To calculate the surface area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular sides.

### Given dimensions:
- **Base of triangle (b)** = 5 cm
- **Height of triangle (h)** = 4 cm
- **Sides of the triangle (side1, side2, side3)** = 8 cm, 6 cm, 9 cm (not directly relevant for surface area, but can help verify whether the given triangular dimensions form a valid triangle)
- **Length of the prism (l)** = 10 cm

### Step 1: Area of triangular base
The area \(A\) of the triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times b \times h
\]
Substituting the values:
\[
A = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 20 \, \text{cm}^2 = 10 \, \text{cm}^2
\]

### Step 2: Total area of triangular bases
Since there are two triangular bases:
\[
\text{Total area of triangular bases} = 2 \times A = 2 \times 10 \, \text{cm}^2 = 20 \, \text{cm}^2
\]

### Step 3: Area of the rectangular sides
The three rectangular sides have the following dimensions:
1. Rectangle area with side 8 cm:
\[
\text{Area}_1 = \text{side} \times \text{length} = 8 \, \text{cm} \times 10 \, \text{cm} = 80 \, \text{cm}^2
\]
2. Rectangle area with side 6 cm:
\[
\text{Area}_2 = 6 \, \text{cm} \times 10 \, \text{cm} = 60 \, \text{cm}^2
\]
3. Rectangle area with side 9 cm:
\[
\text{Area}_3 = 9 \, \text{cm} \times 10 \, \text{cm} = 90 \, \text{cm}^2
\]

### Step 4: Total area of rectangular sides
\[
\text{Total area of rectangles} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 80 \, \text{cm}^2 + 60 \, \text{cm}^2 + 90 \, \text{cm}^2 = 230 \, \text{cm}^2
\]

### Step 5: Total surface area of the prism
\[
\text{Total surface area} = \text{Total area of triangular bases} + \text{Total area of rectangles} = 20 \, \text{cm}^2 + 230 \, \text{cm}^2 = 250 \, \text{cm}^2
\]

### Final Result
The surface area of the triangular prism is \(250 \, \text{cm}^2\).