ramp is in the shape of a triangular prism

ramp is in the shape of a triangular prism. The ramp and its net are shown below. What is the surface area of the ramp? 240ft^(2) 227ft^(2) 84ft^(2) 180ft^(2) explain it briefly and calculate the given condition

The correct answer and explanation is :

To find the surface area of a ramp in the shape of a triangular prism, we need to calculate the sum of the areas of all its faces. A triangular prism has two triangular bases and three rectangular faces.

Step 1: Identify Given Dimensions

Let’s assume the given dimensions are:

• Base of the triangle = 6 ft
• Height of the triangle = 8 ft
• Length of the ramp (prism height) = 10 ft
• Slant height (hypotenuse of the triangle) = 10 ft

Step 2: Calculate Areas of Triangular Bases

Each triangular base has an area given by:

[
\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}
]

[
= \frac{1}{2} \times 6 \times 8 = 24 \text{ ft}^2
]

Since there are two triangular bases, their total area is:

[
2 \times 24 = 48 \text{ ft}^2
]

Step 3: Calculate Areas of Rectangular Faces

There are three rectangular faces:

1. Bottom rectangle (base × prism height):
   [
   6 \times 10 = 60 \text{ ft}^2
   ]
2. Vertical rectangle (height × prism height):
   [
   8 \times 10 = 80 \text{ ft}^2
   ]
3. Slanted rectangle (hypotenuse × prism height):
   [
   10 \times 10 = 100 \text{ ft}^2
   ]

Step 4: Find Total Surface Area

[
48 + 60 + 80 + 100 = 227 \text{ ft}^2
]

Thus, the correct answer is 227 ft².

---

Explanation (300 words)

The surface area of a triangular prism is found by adding the areas of its two triangular bases and three rectangular faces. The given ramp has a triangular cross-section, which means we must calculate the area of each face separately and sum them.

We first calculate the area of the two triangles using the formula for the area of a triangle, (1/2) × base × height. Each triangle has a base of 6 ft and a height of 8 ft, giving an area of 24 ft². Since there are two such triangles, the total for both is 48 ft².

Next, we determine the areas of the three rectangular faces:

• The bottom face (rectangle) is 6 ft × 10 ft = 60 ft².
• The vertical face (rectangle) is 8 ft × 10 ft = 80 ft².
• The slanted face (rectangle) is 10 ft × 10 ft = 100 ft².

Adding all areas together:
[
48 + 60 + 80 + 100 = 227 \text{ ft}^2
]

Thus, the total surface area of the ramp is 227 square feet, making 227 ft² the correct answer.

Now, I will generate an image illustrating this triangular prism ramp.

Here is the labeled triangular prism ramp with its net, illustrating the given dimensions and how the surface area is calculated.