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Question

An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.

What is the surface area of the net of the triangular prism?

(1 point)
a
square centimeters
Remaining Attempts : 2

Answer 1

To calculate the surface area of the triangular prism, we need to find the area of all the faces in the net.

1. Area of the Rectangles:

   • There are three rectangles in the net.
   • The top and bottom rectangles each have dimensions of 10 cm (length) × 5 cm (width).
     • Area of one rectangle = Length × Width = 10 cm × 5 cm = 50 cm².
     • Area of both top and bottom rectangles = 2 × 50 cm² = 100 cm².
   • The middle rectangle also has a length of 10 cm and a width of 5 cm.
     • Area of the middle rectangle = 10 cm × 5 cm = 50 cm².
   • Total area of the rectangles = 100 cm² + 50 cm² = 150 cm².

2. Area of the Triangles:

   • There are two identical triangles on the left and right sides of the middle rectangle.
   • The base of the triangle = 5 cm, and the height of the triangle = 4 cm.
     • Area of one triangle = (Base × Height) / 2 = (5 cm × 4 cm) / 2 = 10 cm².
   • Area of both triangles = 2 × 10 cm² = 20 cm².

3. Total Surface Area:

   • Total surface area of the prism = Total area of rectangles + Total area of triangles.
   • Total surface area = 150 cm² + 20 cm² = 170 cm².

Therefore, the surface area of the net of the triangular prism is 170 square centimeters.