Question
Base length 12 cm
Base width length 6 cm
Height 4 cm
Sides 5 cm
Find the LATERAL surface area of this triangular prism in cm²
Hint Remember, the triangular face is always the true base.
192 cm 2
216 cm 2
45.cm2
76 cm 2
Base width length 6 cm
Height 4 cm
Sides 5 cm
Find the LATERAL surface area of this triangular prism in cm²
Hint Remember, the triangular face is always the true base.
192 cm 2
216 cm 2
45.cm2
76 cm 2
Answers
GPT-4o mini
To find the lateral surface area of a triangular prism, we need to calculate the areas of the three rectangular lateral faces.
Given the dimensions:
- The base of the triangular face: 12 cm
- The height of the triangular face: 4 cm
- The lengths of the sides of the triangular face: 5 cm (we'll assume these are the other two sides of the triangle)
First, let's find the lengths of the three lateral faces:
1. **Face opposite the base (the triangle height):**
- Height of the triangle: 4 cm
- Length: 12 cm (the base length of the triangular face)
- Area = base × height = 12 cm × 4 cm = 48 cm²
2. **Face adjacent to one of the sides of the triangle:**
- Length of one side: 5 cm
- Height (the same as the prism): 4 cm
- Area = base × height = 5 cm × 4 cm = 20 cm²
3. **Face adjacent to the other side of the triangle:**
- This is the other 5 cm side (same calculation):
- Length: 5 cm
- Height: 4 cm
- Area = 5 cm × 4 cm = 20 cm²
Now, let's sum the areas of the three rectangular lateral faces:
- Area of face opposite the base: 48 cm²
- Area of first side face: 20 cm²
- Area of second side face: 20 cm²
Total lateral surface area = 48 cm² + 20 cm² + 20 cm² = 88 cm²
It looks like none of the options provided match the calculated lateral surface area of 88 cm², but if the provided dimensions are considered, perhaps you might want to verify the numbers or the problem setup once more.
Given the dimensions:
- The base of the triangular face: 12 cm
- The height of the triangular face: 4 cm
- The lengths of the sides of the triangular face: 5 cm (we'll assume these are the other two sides of the triangle)
First, let's find the lengths of the three lateral faces:
1. **Face opposite the base (the triangle height):**
- Height of the triangle: 4 cm
- Length: 12 cm (the base length of the triangular face)
- Area = base × height = 12 cm × 4 cm = 48 cm²
2. **Face adjacent to one of the sides of the triangle:**
- Length of one side: 5 cm
- Height (the same as the prism): 4 cm
- Area = base × height = 5 cm × 4 cm = 20 cm²
3. **Face adjacent to the other side of the triangle:**
- This is the other 5 cm side (same calculation):
- Length: 5 cm
- Height: 4 cm
- Area = 5 cm × 4 cm = 20 cm²
Now, let's sum the areas of the three rectangular lateral faces:
- Area of face opposite the base: 48 cm²
- Area of first side face: 20 cm²
- Area of second side face: 20 cm²
Total lateral surface area = 48 cm² + 20 cm² + 20 cm² = 88 cm²
It looks like none of the options provided match the calculated lateral surface area of 88 cm², but if the provided dimensions are considered, perhaps you might want to verify the numbers or the problem setup once more.