Use the image described to answer the question
A triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 8 centimeters. The left side meets the base to form a right angle. The base of the triangle measures 6 centimeters. The hypotenuse side of the triangle measures 10 centimeters. The width of the rectangular face measures 9 centimeters.
what is the surface area of the triangular prism?
__ square centimeters
To find the surface area of a triangular prism, we need to find the areas of all the individual faces and add them together.
1. The area of the front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6 cm * 8 cm
Area = 24 square centimeters
2. The area of the right rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 square centimeters
Since there are two faces of each shape, we multiply by 2 for each:
Front triangular face area = 24 square centimeters
Right rectangular face area = 90 square centimeters
Total surface area = 2(24) + 2(90)
Total surface area = 48 + 180
Total surface area = 228 square centimeters
Therefore, the surface area of the triangular prism is 228 square centimeters.
Use the image to answer the 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?
__ square centimeters
To find the surface area of the net of the triangular prism, we need to calculate the areas of all the individual faces and add them together.
1. The top and bottom rectangles:
Area = length * width
Area = 10 cm * 5 cm = 50 square centimeters for each rectangle. Since there are two rectangles, the total area for the top and bottom rectangles is 2 * 50 = 100 square centimeters.
2. The middle rectangle:
The middle rectangle does not contribute to the surface area of the net.
3. The two triangular faces:
Area of a triangle = (1/2) * base * height
Area of each triangle = (1/2) * 5 cm * 4 cm = 10 square centimeters. Since there are two identical triangles, the total area for both triangles is 2 * 10 = 20 square centimeters.
Therefore, the total surface area of the net of the triangular prism is:
Top and bottom rectangles: 100 square centimeters
Triangular faces: 20 square centimeters
Total surface area = 100 + 20 = 120 square centimeters
Therefore, the surface area of the net of the triangular prism is 120 square centimeters.
not right
Apologies for the mistake in the previous calculation. Let's correct it:
1. The top and bottom rectangles:
Area = length * width = 10 cm * 5 cm = 50 square centimeters for each rectangle. Since there are two rectangles, the total area for the top and bottom rectangles is 2 * 50 = 100 square centimeters.
2. The two triangular faces:
The base of the triangle is 5 cm, and the height is 4 cm.
Area of each triangle = (1/2) * base * height = (1/2) * 5 cm * 4 cm = 10 square centimeters. Since there are two identical triangles, the total area for both triangles is 2 * 10 = 20 square centimeters.
Therefore, the total surface area of the net of the triangular prism is:
Top and bottom rectangles: 100 square centimeters
Triangular faces: 20 square centimeters
Total surface area = 100 + 20 = 120 square centimeters
Therefore, the correct surface area of the net of the triangular prism is 120 square centimeters.