Surface Area of Triangular Prisms Quick Check4 of 54 of 5 ItemsQuestionUse the image to answer the question.An illustration shows 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 and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.What is the surface area of the net of the triangular prism?(1 point)Responses768 square meters768 square meters790 square meters790 square meters779 square meters779 square meters822 square meters
wrong
I apologize for the mistake. Let's try solving it again.
1. Area of the front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 16 * 15
Area = 120 square meters
2. Area of the right rectangular face:
Area = length * width
Area = 17 * 11
Area = 187 square meters
3. Area of the left rectangular face (same as the right rectangular face):
Area = 187 square meters
4. Area of the top rectangular face:
Area = base * width
Area = 16 * 11
Area = 176 square meters
5. Area of the bottom rectangular face (same as the top rectangular face):
Area = 176 square meters
Now, add the areas of all five faces together:
120 + 187 + 187 + 176 + 176 = 846 square meters
Therefore, the surface area of the net of the triangular prism is 846 square meters.
whats 494x2
494 multiplied by 2 is equal to 988.
Therefore, the surface area of the net of the triangular prism is 988 square meters. Thank you for pointing out the calculation error.
Surface Area of Triangular Prisms Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows 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 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?
(1 point)
Responses
17 cm
17 cm
16 cm
16 cm
10 cm
10 cm
8 cm
To find the missing length "l" of the triangular prism, we first need to calculate the surface area of the prism using the given measurements:
1. Area of the front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 8 * 6
Area = 24 square centimeters
2. Area of the right rectangular face:
Since the width of the right rectangular face is not given, let the width be "w" cm.
Area = length * width
Area = 10 * w
Area = 10w square centimeters
3. Given that the total surface area is 524 square centimeters, the sum of all faces' areas should be equal to 524 square centimeters:
524 = 24 + 10w + 10w + l + l
524 = 24 + 20w + 2l
Now, we need to solve for "l":
2l = 524 - 24 - 20w
2l = 500 - 20w
l = 250 - 10w
Since both the sides of the triangle are 10 cm each, and the base of the triangle is 8 cm, the missing length "l" must be equal to the base of the triangle. Therefore, the missing length "l" is 8 cm.
So, the correct answer is:
8 cm
To find the surface area of the net of the triangular prism, you need to find the area of each individual face and then add them together.
1. Area of the front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 16 * 15
Area = 120 square meters
2. Area of the right rectangular face:
Area = length * width
Area = 17 * 11
Area = 187 square meters
3. Area of the left rectangular face (same as the right rectangular face):
Area = 187 square meters
Now, add the areas of all three faces together:
120 + 187 + 187 = 494 square meters
Therefore, the surface area of the net of the triangular prism is 494 square meters.