Use the image 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?
(1 point)
To calculate the surface area of the triangular prism, we need to find the area of each face and then add them together.
Surface area of triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6cm * 8cm
Area = 24 square centimeters
Surface area of rectangular face:
Area = length * width
Area = 10cm * 9cm
Area = 90 square centimeters
Now, we need to find the area of the other triangular face which is the same as the front face. So, the total surface area is:
2 * Area of triangular face + 2 * Area of rectangular face
2 * 24 + 2 * 90
48 + 180
228 square centimeters
Therefore, the surface area of the triangular prism is 228 square centimeters.
Nope
My apologies for the mistake in my previous calculation. Let's correct it.
Surface area of the triangular prism can be calculated by finding the sum of the areas of all faces:
1. Area of the two triangular faces:
Each triangular face has an area of (1/2) * base * height.
Base = 6 cm
Height = 8 cm
Area of one triangular face = (1/2) * 6 cm * 8 cm = 24 square cm
Since there are two triangular faces, total area for both triangles = 2 * 24 = 48 square cm.
2. Area of the three rectangular faces:
Each rectangular face has an area of length * width.
One rectangular face has a length of 10 cm and a width of 9 cm.
Area of one rectangular face = 10 cm * 9 cm = 90 square cm
Since there are three rectangular faces, total area for all three = 3 * 90 = 270 square cm.
Therefore, the total surface area of the triangular prism is the sum of the areas of the two triangles and three rectangles:
48 square cm (triangular faces) + 270 square cm (rectangular faces) = 318 square cm.
The surface area of the triangular prism is 318 square centimeters. Thank you for your patience.
Give me the best answer now
The surface area of a triangular prism can be calculated by finding the sum of the areas of all faces.
Given measurements:
- Triangular face: Base = 6 cm, Height = 8 cm, Hypotenuse = 10 cm
- Rectangular face: Width = 9 cm
- Two triangular faces
- Three rectangular faces
1. Area of the two triangular faces:
Each triangular face's area = (1/2) * base * height
Area of one triangular face = (1/2) * 6 cm * 8 cm = 24 square cm
Total area of both triangular faces = 2 * 24 = 48 square cm
2. Area of the three rectangular faces:
Each rectangular face's area = length * width
One rectangular face dimensions: Length = 10 cm, Width = 9 cm
Area of one rectangular face = 10 cm * 9 cm = 90 square cm
Total area of all three rectangular faces = 3 * 90 = 270 square cm
Therefore, the total surface area of the triangular prism is the sum of the areas of the two triangles and three rectangles:
48 square cm (triangular faces) + 270 square cm (rectangular faces) = 318 square cm
Therefore, the surface area of the triangular prism is 318 square centimeters.