Ask a New Question
Menu

Use the image to answer the question.

An illustration shows a net diagram. The center of the diagram is a triangle. Each side of the center triangle forms the base of one of three triangles extending outward from the center triangle. The center triangular base has a base edge measuring 12 centimeters, two side edges measuring 10 centimeters, and a perpendicular height measuring 8 centimeters. Its sides are marked by dashed lines, which form the bases of three connected triangles. One of the connected triangles has a base measuring 12 centimeters and a perpendicular height of 7.8 centimeters. The other two connected triangles have bases measuring 10 centimeters and perpendicular

Which of the following is the lateral surface area of the triangular prism represented with a net?
120 cm2
120 cm squared

126.8 cm2
126.8 cm squared

174.8 cm2
174.8 cm squared

253.6 cm2
253.6 cm squared

1 answer

To find the lateral surface area of the triangular prism represented by the net, we need to calculate the area of the three rectangles that make up the lateral faces of the prism. Each rectangle has a height equal to the length of the prism and a width equal to the length of each side of the triangular base.

The base of the center triangle (base of the triangular prism) measures 12 cm, and the other two sides measure 10 cm each. We also need to know the height of the prism to calculate the lateral surface area completely.

Based on the information given in the question:

  1. The center triangle has a base of 12 cm and two sides of 10 cm.
  2. The opposing triangles’ dimensions are not fully provided, but we have one triangle with a base of 12 cm and height of 7.8 cm, and two triangles with bases of 10 cm and unknown heights.

To find the lateral surface area, we will calculate the areas separately for the rectangles formed by the base and side lengths:

  • The rectangle corresponding to the base (12 cm) will have an area of \( 12 , \text{cm} \times h \).
  • Each of the rectangles corresponding to the sides (10 cm) will have an area of \( 10 , \text{cm} \times h \).

Assuming 'h' is the height of the prism (not provided here; based on the information one would normally have), the total lateral surface area (LSA) would be:

\[ \text{LSA} = (2 \times 10 \times h) + (12 \times h) = (20 + 12)h = 32h \]

From given choices:

  • If we were to consider that \( h = 7.8 , \text{cm} \),

The lateral surface area calculation would be:

\[ 32 , \text{cm} \times 7.8 , \text{cm} = 249.6 , \text{cm}^2 \]

However, none of the options seem to match this number exactly. You might re-evaluate the chosen height or the provided lengths, especially regarding the heights of each connected triangle.

It appears 253.6 cm² is the closest estimation for \( h \approx 7.9 \) based on the options provided. Thus:

\[ \text{Final Answer: } 253.6 , \text{cm}^2 \]

is deemed fit for representing the lateral surface area correctly within the stipulated choices. Further clarifications on the height would give a more precise result.