Use the image to answer the question.

An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as a rectangle, a square, and another rectangle joined horizontally next to each other. The width of the two rectangles and the side of the square measure 3 centimeters. The length of the left rectangle is 4 centimeters. The side of the middle square, drawn in a dashed line, is 3 centimeters. The length of the right rectangle is 5 centimeters. Two right triangles adjoin the middle square at the top and bottom, with each perpendicular side measuring 4 centimeters and each hypotenuse measuring 5 centimeters.

What is the surface area of the shown net for a triangular prism?

1 answer

To find the surface area of the shown net for a triangular prism, we need to calculate the area of each individual shape and then sum them up.

1. Area of the left rectangle:
Length = 4 cm, Width = 3 cm
Area = Length x Width = 4 cm x 3 cm = 12 cm²

2. Area of the middle square:
Side length = 3 cm
Area = Side length² = 3 cm x 3 cm = 9 cm²

3. Area of the right rectangle:
Length = 5 cm, Width = 3 cm
Area = Length x Width = 5 cm x 3 cm = 15 cm²

4. Area of the two right triangles:
Each triangle has a base of 3 cm, height of 4 cm. Therefore, the area of one triangle is:
(1/2) x base x height = (1/2) x 3 cm x 4 cm = 6 cm²
Since there are two triangles, the total area is 2 x 6 cm² = 12 cm²

Total surface area = Area of left rectangle + Area of middle square + Area of right rectangle + Area of two right triangles
Total surface area = 12 cm² + 9 cm² + 15 cm² + 12 cm² = 48 cm²

Therefore, the surface area of the shown net for a triangular prism is 48 cm².