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.
The total surface area represented by this net of a triangular prism can be calculated by finding the area of each face and adding them together. There are five faces to consider:
1. The bottom triangle has area 1/2 * base * height = 1/2 * 9 cm * 17 cm = 76.5 cm².
2. The top triangle has the same area as the bottom triangle.
3. The front rectangle has area length * width = 17 cm * 9 cm = 153 cm².
4. The back rectangle has the same area as the front rectangle.
5. The side triangle has area 1/2 * base * height = 1/2 * 7.8 cm * 9 cm = 35.1 cm².
Adding these areas together, we get a total surface area of 76.5 cm² + 76.5 cm² + 153 cm² + 153 cm² + 35.1 cm² = 494.1 cm².
Therefore, the total surface area represented by this net of a triangular prism is 494.1 cm².
it said the answer should have 2 decimal places.
Sorry about that, here's the revised answer with two decimal places:
The total surface area represented by this net of a triangular prism can be calculated by finding the area of each face and adding them together. There are five faces to consider:
1. The bottom triangle has area 1/2 * base * height = 1/2 * 9 cm * 17 cm = 76.50 cm².
2. The top triangle has the same area as the bottom triangle.
3. The front rectangle has area length * width = 17 cm * 9 cm = 153 cm².
4. The back rectangle has the same area as the front rectangle.
5. The side triangle has area 1/2 * base * height = 1/2 * 7.8 cm * 9 cm = 35.10 cm².
Adding these areas together, we get a total surface area of 76.50 cm² + 76.50 cm² + 153.00 cm² + 153.00 cm² + 35.10 cm² = 494.60 cm².
Therefore, the total surface area represented by this net of a triangular prism is 494.60 cm² with two decimal places.
To find the total surface area of the net, we need to sum up the areas of all the visible faces.
1. The area of the middle triangle can be calculated using the formula: A = (base * height) / 2. In this case, the base is 9 centimeters and the height is 7.8 centimeters. Therefore, the area of this triangle is (9 * 7.8) / 2 = 35.1 square centimeters.
2. The areas of the two rectangles can be calculated using the formula: A = length * width. In this case, the length is 17 centimeters and the width is 9 centimeters. Therefore, the area of each rectangle is 17 * 9 = 153 square centimeters. Since there are two rectangles, the total area of the rectangles is 2 * 153 = 306 square centimeters.
Adding the areas of the triangle and rectangles together, we get a total surface area of 35.1 + 306 = 341.1 square centimeters.
So, the total surface area represented by this net of a triangular prism is 341.1 square centimeters.
To find the total surface area of the triangular prism, we need to calculate the areas of all the individual faces and then add them up.
Step 1: Triangular Face
The triangular face in the middle has two legs that are each labeled as 9 centimeters. To find the area of a triangle, we can use the formula:
Area = (base * height) / 2
Since the base and height of the triangle are both 9 centimeters, we can substitute these values into the formula:
Area = (9 * 9) / 2 = 81 / 2 = 40.5 square centimeters
Step 2: Rectangular Faces
The net shows two rectangular faces, each with dimensions labeled as length and width. The length is given as 17 centimeters, and the width is given as 9 centimeters. To find the area of a rectangle, we multiply length by width.
Area of each rectangular face = length * width
= 17 * 9
= 153 square centimeters
Since there are two identical rectangular faces, the total area for both faces will be:
Total area of rectangular faces = 2 * Area of each rectangular face
= 2 * 153
= 306 square centimeters
Step 3: Triangular Face on the Side
The net shows another triangular face attached to one of the rectangles, opposite to the middle triangle. The vertical height of this triangle is given as 7.8 centimeters.
To find its area, we use the same formula as before:
Area = (base * height) / 2
Since the base of the triangle is 17 centimeters (the same as the width of the rectangle), we can substitute these values into the formula:
Area = (17 * 7.8) / 2 = 132.6 / 2 = 66.3 square centimeters
Step 4: Total Surface Area
To find the total surface area, we add up all the areas we calculated:
Total Surface Area = Area of triangular face + Total area of rectangular faces + Area of triangular face on the side
= 40.5 + 306 + 66.3
= 412.8 square centimeters
Therefore, the total surface area represented by this net of a triangular prism is 412.8 square centimeters.