Use the image to answer the question.
An illustration shows a triangular prism placed sideways with one of its rectangular faces as the base. Dimensions are labeled. The length and width of the rectangular base are 17 centimeters and 13 centimeters respectively. The face visible in front appears as a triangle. The base width of the triangle is 13 centimeters. The perpendicular leg of the triangle is 7.48 centimeters and the slanting leg (hypotenuse) is 15 centimeters. The edges that are not visible are represented by dashed lines.
Apply the technique of using nets to find the surface area of this triangular prism. Your answer should have two decimal places.
A:700.40 cm2
B:97.24 cm2
C:603.16 cm2
D:573.24 cm2
C: 603.16 cm2
To find the surface area of the triangular prism using nets, we need to calculate the areas of each face and then add them together.
1. The rectangular base has a length of 17 cm and a width of 13 cm. The area of the rectangular base is given by the formula:
Area of rectangular base = length × width = 17 cm × 13 cm = 221 cm².
2. The front face is a triangle with a base width of 13 cm, a perpendicular leg of 7.48 cm, and a hypotenuse (slanting leg) of 15 cm. We can find the area of this triangle using the formula:
Area of triangle = 0.5 × base × height = 0.5 × 13 cm × 7.48 cm = 48.62 cm².
3. The back face is the same as the front face, so it also has an area of 48.62 cm².
4. The two remaining faces on the sides are both rectangles with dimensions equal to the height of the prism (the dimension that is not given in the image). Unfortunately, we cannot determine the height from the given information and image.
Since we cannot determine the height, we cannot calculate the areas of the two side faces. Therefore, we can only calculate the total surface area by adding the areas of the rectangular base and the two triangular faces.
Total surface area = Area of rectangular base + Area of front triangle + Area of back triangle
Total surface area = 221 cm² + 2 × 48.62 cm²
Total surface area ≈ 318.24 cm².
Since we are asked to provide the answer with two decimal places, the correct option is:
D: 573.24 cm².