To find the surface area of the triangular prism, we first need to find the area of each individual shape on the net.
1. The middle parallelogram has dimensions of 4 cm (width) and 12 cm (length), so its area is 4 cm x 12 cm = 48 square cm.
2. The two right triangles each have an area of 1/2 x base x height, so each triangle has an area of 1/2 x 12 cm x 9 cm = 54 square cm. Since there are two triangles, the total area of the triangles is 2 x 54 square cm = 108 square cm.
Now, we add up the areas of all the shapes to find the total surface area of the triangular prism.
Surface area = 2 x area of middle parallelogram + 2 x area of right triangle = 2 x 48 square cm + 108 square cm = 96 square cm + 108 square cm = 204 square cm.
Therefore, the surface area of the triangular prism is 204 square cm.
Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three horizontal parallelograms joined next to each other. All 4 sides of the middle parallelogram are drawn with dashed lines. The width of the parallelograms is 4 centimeters. The length of the middle parallelogram is 12 centimeters. Two right triangles adjoin the middle parallelogram on the top and bottom 12 centimeter sides, with their hypotenuse sides measuring 15 centimeters and the perpendicular sides measuring 9 centimeters. Right angles are shown at the intersection of the perpendicular sides and the base sides of the triangles.
What is the surface area of the triangular prism whose net is shown?
(1 point)
Responses
9 answers
nope
I apologize for the error in my previous response. Let's try to calculate the surface area of the triangular prism again.
The surface area of a triangular prism consists of three pairs of congruent parallelograms (two bases and one lateral side).
Given that the width of the parallelograms is 4 cm, the height of the right triangles is 9 cm, and the base length is 12 cm, we can calculate the surface area as follows:
1. Area of the two bases:
Base Area = 2 * (1/2 * base * height) = 2 * (1/2 * 12 cm * 9 cm) = 2 * 54 sq cm = 108 sq cm
2. Area of the lateral side (middle parallelogram):
Lateral Side Area = length * width = 12 cm * 4 cm = 48 sq cm
3. Total Surface Area:
Total Surface Area = 2 * Base Area + Lateral Side Area = 2 * 108 sq cm + 48 sq cm = 216 sq cm + 48 sq cm = 264 sq cm
Therefore, the surface area of the triangular prism, based on the given dimensions, is 264 square centimeters.
The surface area of a triangular prism consists of three pairs of congruent parallelograms (two bases and one lateral side).
Given that the width of the parallelograms is 4 cm, the height of the right triangles is 9 cm, and the base length is 12 cm, we can calculate the surface area as follows:
1. Area of the two bases:
Base Area = 2 * (1/2 * base * height) = 2 * (1/2 * 12 cm * 9 cm) = 2 * 54 sq cm = 108 sq cm
2. Area of the lateral side (middle parallelogram):
Lateral Side Area = length * width = 12 cm * 4 cm = 48 sq cm
3. Total Surface Area:
Total Surface Area = 2 * Base Area + Lateral Side Area = 2 * 108 sq cm + 48 sq cm = 216 sq cm + 48 sq cm = 264 sq cm
Therefore, the surface area of the triangular prism, based on the given dimensions, is 264 square centimeters.
no these are ur choices
198 cm2
198 cm squared
108 cm2
108 cm squared
216 cm2
216 cm squared
252 cm2
198 cm2
198 cm squared
108 cm2
108 cm squared
216 cm2
216 cm squared
252 cm2
Let's calculate the surface area of the triangular prism based on the given net illustration.
1. The base area:
The base is a right triangle with base 12 cm and height 9 cm. The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. The lateral area:
The middle parallelogram has a width of 4 cm and a length of 12 cm. The area of the middle parallelogram is length * width = 12 cm * 4 cm = 48 square cm. Since there are two identical sides, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
The surface area of the triangular prism is the sum of the base area and the lateral area:
Total Surface Area = Base Area + Lateral Area = 108 square cm + 96 square cm = 204 square cm
Therefore, the surface area of the triangular prism based on the given dimensions is 204 square cm.
1. The base area:
The base is a right triangle with base 12 cm and height 9 cm. The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. The lateral area:
The middle parallelogram has a width of 4 cm and a length of 12 cm. The area of the middle parallelogram is length * width = 12 cm * 4 cm = 48 square cm. Since there are two identical sides, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
The surface area of the triangular prism is the sum of the base area and the lateral area:
Total Surface Area = Base Area + Lateral Area = 108 square cm + 96 square cm = 204 square cm
Therefore, the surface area of the triangular prism based on the given dimensions is 204 square cm.
that is WRONG
Apologies for the previous errors. Let's calculate the surface area of the triangular prism based on the given net.
1. Base area:
The base of the triangular prism is a right triangle with base 12 cm and height 9 cm. The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two such triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. Lateral area:
The lateral faces of the triangular prism are the three parallelograms. The middle parallelogram has a length of 12 cm and a width of 4 cm, giving an area of 12 cm * 4 cm = 48 square cm. Since there are two identical lateral faces, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
Adding the base area and the lateral area:
Total Surface Area = Base Area + Lateral Area
Total Surface Area = 108 square cm + 96 square cm
Total Surface Area = 204 square cm
Therefore, the correct surface area of the triangular prism based on the given dimensions is 204 square cm.
1. Base area:
The base of the triangular prism is a right triangle with base 12 cm and height 9 cm. The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two such triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. Lateral area:
The lateral faces of the triangular prism are the three parallelograms. The middle parallelogram has a length of 12 cm and a width of 4 cm, giving an area of 12 cm * 4 cm = 48 square cm. Since there are two identical lateral faces, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
Adding the base area and the lateral area:
Total Surface Area = Base Area + Lateral Area
Total Surface Area = 108 square cm + 96 square cm
Total Surface Area = 204 square cm
Therefore, the correct surface area of the triangular prism based on the given dimensions is 204 square cm.
NO PICK FROM THE CHOICES I GAVE YOU
I apologize for the oversight. Let's go through the calculations once more based on the choices you provided.
Given the choices are:
1. 198 cm^2
2. 108 cm^2
3. 216 cm^2
4. 252 cm^2
Calculating the surface area of the triangular prism:
1. Base Area:
The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two such triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. Lateral Area:
The middle parallelogram has a length of 12 cm and a width of 4 cm, giving an area of 12 cm * 4 cm = 48 square cm. Since there are two identical lateral faces, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
Total Surface Area = Base Area + Lateral Area
Total Surface Area = 108 square cm + 96 square cm
Total Surface Area = 204 square cm
Based on the given choices, the closest option to the calculated surface area is 198 cm^2.
Therefore, the surface area of the triangular prism, based on the given net illustration and dimensions, is approximately 198 cm^2. Thank you for your patience.
Given the choices are:
1. 198 cm^2
2. 108 cm^2
3. 216 cm^2
4. 252 cm^2
Calculating the surface area of the triangular prism:
1. Base Area:
The area of one triangle is 1/2 * base * height = 1/2 * 12 cm * 9 cm = 54 square cm. Since there are two such triangles (top and bottom), the total area of the bases is 2 * 54 square cm = 108 square cm.
2. Lateral Area:
The middle parallelogram has a length of 12 cm and a width of 4 cm, giving an area of 12 cm * 4 cm = 48 square cm. Since there are two identical lateral faces, the total lateral area is 2 * 48 square cm = 96 square cm.
3. Total Surface Area:
Total Surface Area = Base Area + Lateral Area
Total Surface Area = 108 square cm + 96 square cm
Total Surface Area = 204 square cm
Based on the given choices, the closest option to the calculated surface area is 198 cm^2.
Therefore, the surface area of the triangular prism, based on the given net illustration and dimensions, is approximately 198 cm^2. Thank you for your patience.