Coordinate Geometry and Nets Unit Test
13 of 1513 of 15 Items
Question
Use the image to answer the question.
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as a triangle in the middle attached to a rectangle on each side. The sides of two legs of the triangle are each labeled 9 centimeters. The length and width of the rectangles is 17 centimeters and 9 centimeters respectively. Another triangle of vertical height 7.8 centimeters is attached to one of the rectangles, opposite to the middle triangle.
What is the total surface area represented by this net of a triangular prism? Your answer should have two decimal places.
(1 point)
cm2
The total surface area can be calculated by finding the areas of the individual shapes and then adding them together.
The area of the triangle in the middle can be calculated using the formula for the area of a triangle: (base * height) / 2
Area = (9 * 7.8) / 2 = 35.1 cm^2
The area of each rectangle can be calculated using the formula for the area of a rectangle: length * width
Area = 17 * 9 = 153 cm^2 (There are two rectangles, so the total area for both rectangles is 306 cm^2)
The two side triangles are congruent to the middle triangle, so the total area for both side triangles is also 35.1 cm^2.
Now, add all the areas together to find the total surface area:
35.1 (middle triangle) + 306 (two rectangles) + 35.1 (two side triangles) = 376.2 cm^2
Therefore, the total surface area represented by this net of a triangular prism is 376.2 cm^2.
no
I apologize for that mistake. Let's correct the calculation:
The net consists of:
- 2 triangles with base 9 cm and height 7.8 cm each
- 2 rectangles with length 17 cm and width 9 cm each
- 1 large rectangle with base 17 cm and height 7.8 cm
Calculating the areas of each shape:
- Area of each triangle = (1/2) * base * height
Area of each triangle = (1/2) * 9 * 7.8 = 35.1 cm^2 (for each triangle)
- Area of each rectangle = length * width
Area of each rectangle = 17 * 9 = 153 cm^2 (for each rectangle)
Total area for both rectangles = 2 * 153 = 306 cm^2
- Area of the large rectangle = 17 * 7.8 = 132.6 cm^2
Now, calculate the total surface area:
35.1 (two triangles) + 306 (two rectangles) + 132.6 (large rectangle) = 473.7 cm^2
Therefore, the total surface area represented by this net of a triangular prism is 473.7 cm^2. Thank you for your patience.