To find the surface area of a triangular prism, we need to calculate the area of each of the individual faces and then sum them up.
1. Start with the two triangular faces:
Area of a triangle = 1/2 * base * height
Area of the triangle with base s1 and height h: 1/2 * 10 * 9 = 45 sq inches
Area of the triangle with base s2 and height h: 1/2 * 12 * 9 = 54 sq inches
2. Next, calculate the area of the three rectangular faces:
Area of a rectangle = length * width
Area of the rectangular face with length l and width s1: 10 * 10 = 100 sq inches
Area of the rectangular face with length l and width s2: 10 * 12 = 120 sq inches
Area of the rectangular face with length l and width s3: 10 * 17 = 170 sq inches
3. Sum up all the individual areas to find the total surface area of the triangular prism:
45 + 54 + 100 + 120 + 170 = 489 sq inches
Therefore, the surface area of the display showcase is 489 square inches.
Christian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h =9 inches, b =17 inches, s1 =10 inches, s2 =12 inches, s3 = 17 and l =10 inches.(1 point) S.A.= in.2..
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wrong Christian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: height =9 inches, base =17 inches, side 1 =10 inches, side 2 =12 inches, side 3 = 17 and length =10 inches.(1 point) Surface Area.= in.2
To find the surface area of a triangular prism, we need to calculate the areas of the individual faces and add them up.
1. Calculate the area of one of the triangular faces:
Area of a triangle = 1/2 * base * height
Area of the triangle with base s1 = 10 inches and height h = 9 inches:
1/2 * 10 * 9 = 45 square inches
2. Calculate the area of the other triangular face:
Area of the triangle with base s2 = 12 inches and height h = 9 inches:
1/2 * 12 * 9 = 54 square inches
3. Calculate the area of the three rectangular faces:
- The rectangular face with length l = 10 inches and width s1 = 10 inches:
10 * 10 = 100 square inches
- The rectangular face with length l = 10 inches and width s2 = 12 inches:
10 * 12 = 120 square inches
- The rectangular face with length l = 10 inches and width s3 = 17 inches:
10 * 17 = 170 square inches
4. Add up the areas of all faces to find the total surface area of the triangular prism:
45 + 54 + 100 + 120 + 170 = 489 square inches
Therefore, the surface area of the display showcase is 489 square inches.
1. Calculate the area of one of the triangular faces:
Area of a triangle = 1/2 * base * height
Area of the triangle with base s1 = 10 inches and height h = 9 inches:
1/2 * 10 * 9 = 45 square inches
2. Calculate the area of the other triangular face:
Area of the triangle with base s2 = 12 inches and height h = 9 inches:
1/2 * 12 * 9 = 54 square inches
3. Calculate the area of the three rectangular faces:
- The rectangular face with length l = 10 inches and width s1 = 10 inches:
10 * 10 = 100 square inches
- The rectangular face with length l = 10 inches and width s2 = 12 inches:
10 * 12 = 120 square inches
- The rectangular face with length l = 10 inches and width s3 = 17 inches:
10 * 17 = 170 square inches
4. Add up the areas of all faces to find the total surface area of the triangular prism:
45 + 54 + 100 + 120 + 170 = 489 square inches
Therefore, the surface area of the display showcase is 489 square inches.
same as last answer and its still wrong your name is ai artificial intelligence your supposed to be smart especially in math
I apologize for the mistake in my previous responses. Let's calculate the surface area of the triangular prism correctly this time.
The surface area of a triangular prism can be calculated by finding the sum of the areas of its two triangular bases and three rectangular faces.
1. Area of the two triangular bases:
- Area of a triangle = 1/2 * base * height
- Area of the first base = 1/2 * 10 * 9 = 45 square inches
- Area of the second base = 1/2 * 12 * 9 = 54 square inches
2. Area of the three rectangular faces:
- Area of the face with dimensions 10 x 17 = 10 * 17 = 170 square inches
- Area of the face with dimensions 10 x 12 = 10 * 12 = 120 square inches
- Area of the face with dimensions 17 x 12 = 17 * 12 = 204 square inches
3. Calculate the total surface area by summing the areas of all faces:
Total surface area = 45 (1st base) + 54 (2nd base) + 170 (rectangular face 1) + 120 (rectangular face 2) + 204 (rectangular face 3)
Total surface area = 45 + 54 + 170 + 120 + 204
Total surface area = 593 square inches
Therefore, the correct surface area of the display showcase in this case is 593 square inches. Thank you for your patience.
The surface area of a triangular prism can be calculated by finding the sum of the areas of its two triangular bases and three rectangular faces.
1. Area of the two triangular bases:
- Area of a triangle = 1/2 * base * height
- Area of the first base = 1/2 * 10 * 9 = 45 square inches
- Area of the second base = 1/2 * 12 * 9 = 54 square inches
2. Area of the three rectangular faces:
- Area of the face with dimensions 10 x 17 = 10 * 17 = 170 square inches
- Area of the face with dimensions 10 x 12 = 10 * 12 = 120 square inches
- Area of the face with dimensions 17 x 12 = 17 * 12 = 204 square inches
3. Calculate the total surface area by summing the areas of all faces:
Total surface area = 45 (1st base) + 54 (2nd base) + 170 (rectangular face 1) + 120 (rectangular face 2) + 204 (rectangular face 3)
Total surface area = 45 + 54 + 170 + 120 + 204
Total surface area = 593 square inches
Therefore, the correct surface area of the display showcase in this case is 593 square inches. Thank you for your patience.
its wrong just give me the correct one its 7th grade math not 9th grade math
I apologize for the previous errors. Let's simplify the calculation and find the correct surface area of the triangular prism based on the given dimensions:
Given:
Height (h) = 9 inches
Base (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of the triangular prism, we need to calculate the area of each face and add them up:
1. Two triangular faces:
Area of a triangle = 1/2 * base * height
First triangular face: 1/2 * 10 * 9 = 45 square inches
Second triangular face: 1/2 * 12 * 9 = 54 square inches
2. Three rectangular faces:
Face 1: length * width = 10 * 17 = 170 square inches
Face 2: 10 * 12 = 120 square inches
Face 3: 10 * 17 = 170 square inches
Now, calculate the total surface area:
Total surface area = 45 (1st triangular face) + 54 (2nd triangular face) + 170 (rectangular face 1) + 120 (rectangular face 2) + 170 (rectangular face 3)
Total surface area = 559 square inches
Therefore, the correct surface area of the display showcase is 559 square inches. Thank you for your patience, and I apologize for the previous errors.
Given:
Height (h) = 9 inches
Base (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of the triangular prism, we need to calculate the area of each face and add them up:
1. Two triangular faces:
Area of a triangle = 1/2 * base * height
First triangular face: 1/2 * 10 * 9 = 45 square inches
Second triangular face: 1/2 * 12 * 9 = 54 square inches
2. Three rectangular faces:
Face 1: length * width = 10 * 17 = 170 square inches
Face 2: 10 * 12 = 120 square inches
Face 3: 10 * 17 = 170 square inches
Now, calculate the total surface area:
Total surface area = 45 (1st triangular face) + 54 (2nd triangular face) + 170 (rectangular face 1) + 120 (rectangular face 2) + 170 (rectangular face 3)
Total surface area = 559 square inches
Therefore, the correct surface area of the display showcase is 559 square inches. Thank you for your patience, and I apologize for the previous errors.
WRONG GIVE ME THE DANG CORRECT ANSWERs
I apologize for the errors in the previous responses. Let's calculate the surface area of the triangular prism with the given dimensions:
Given:
Height (h) = 9 inches
Base (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of a triangular prism, we first need to calculate the area of each face and then sum them up:
1. Area of the two triangular faces:
First triangular face: Area = 1/2 * base * height = 1/2 * 10 * 9 = 45 square inches
Second triangular face: Area = 1/2 * base * height = 1/2 * 12 * 9 = 54 square inches
2. Area of the three rectangular faces:
Rectangular face 1: Area = length * width = 10 * 17 = 170 square inches
Rectangular face 2: Area = length * width = 10 * 12 = 120 square inches
Rectangular face 3: Area = length * width = 10 * 17 = 170 square inches
Total surface area = Sum of all the areas
Total surface area = 45 (1st triangular face) + 54 (2nd triangular face) + 170 (rectangular face 1) + 120 (rectangular face 2) + 170 (rectangular face 3)
Total surface area = 45 + 54 + 170 + 120 + 170
Total surface area = 559 square inches
Therefore, the correct surface area of the display showcase in this case is 559 square inches. Thank you for your patience.
Given:
Height (h) = 9 inches
Base (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of a triangular prism, we first need to calculate the area of each face and then sum them up:
1. Area of the two triangular faces:
First triangular face: Area = 1/2 * base * height = 1/2 * 10 * 9 = 45 square inches
Second triangular face: Area = 1/2 * base * height = 1/2 * 12 * 9 = 54 square inches
2. Area of the three rectangular faces:
Rectangular face 1: Area = length * width = 10 * 17 = 170 square inches
Rectangular face 2: Area = length * width = 10 * 12 = 120 square inches
Rectangular face 3: Area = length * width = 10 * 17 = 170 square inches
Total surface area = Sum of all the areas
Total surface area = 45 (1st triangular face) + 54 (2nd triangular face) + 170 (rectangular face 1) + 120 (rectangular face 2) + 170 (rectangular face 3)
Total surface area = 45 + 54 + 170 + 120 + 170
Total surface area = 559 square inches
Therefore, the correct surface area of the display showcase in this case is 559 square inches. Thank you for your patience.
1 answer