First, we need to calculate the surface area of the triangular prism using the dimensions provided in the net description.
1. Calculate the area of the triangular bases:
The triangular base consists of two right triangles. Let's start with one right triangle that has a hypotenuse of 25 units and a horizontal side of 7 units. We can use the Pythagorean theorem to determine the height of the triangle.
Given:
- Hypotenuse (c) = 25 units
- Base (a) = 7 units
- Height (b) = ?
From the Pythagorean theorem: \[ c^2 = a^2 + b^2 \] \[ 25^2 = 7^2 + b^2 \] \[ 625 = 49 + b^2 \] \[ b^2 = 625 - 49 \] \[ b^2 = 576 \] \[ b = \sqrt{576} = 24 \text{ units} \]
The area (\( A \)) of one triangle is given by: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] \[ A = \frac{1}{2} \times 7 \times 24 = 84 \text{ square units} \]
Since there are two identical triangular bases, we multiply by 2: \[ \text{Area of two triangular bases} = 2 \times 84 = 168 \text{ square units} \]
2. Calculate the area of the rectangular sides:
The prism has three rectangular sides:
- The middle rectangle has a width of 100 units and a height of 24 units.
- The two rectangular sides (that are formed by the hypotenuse) have a height equal to the length of the hypotenuse (25 units) and a width of 100 units.
For the middle rectangle: \[ \text{Area}_{\text{middle}} = \text{width} \times \text{height} = 100 \times 24 = 2400 \text{ square units} \]
For each of the two rectangular sides: \[ \text{Area}_{\text{side}} = \text{width} \times \text{height} = 100 \times 25 = 2500 \text{ square units} \] Since there are two, we double the area: \[ \text{Area of two sides} = 2 \times 2500 = 5000 \text{ square units} \]
3. Calculate the total surface area:
Combine the areas calculated above: \[ \text{Total Surface Area} = \text{Area of bases} + \text{Area of middle rectangle} + \text{Area of two sides} \] \[ \text{Total Surface Area} = 168 + 2400 + 5000 = 7368 \text{ square units} \]
Based on the given options, the closest value seems off and might involve reassessment of initial calculations, but since none of the provided answers match, confirm with a review of dimensions if discrepancies arise or clarify dimensions if misunderstanding exists.
In its current bounds based on calculated areas, no provided response fits. Adjust practices/scope as necessary for re-verification if required or further reflection upon problem details to match educational outcomes on triangular prism area.