Surface Area of Triangular Prisms Quick Check
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Question
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
216 cm2
, , 216 cm squared
252 cm2
252 cm squared
108 cm2
, 108 cm squared
198 cm2
, 198 cm squared
.....
Wow
Surface Area of Triangular Prisms Quick Check
1 of 51 of 5 Items
Question
What is a two-dimensional representation of a three-dimensional figure?(1 point)
Responses
a rectangle
a rectangle
a triangle
a triangle
a net
a net
a triangular prism
a triangular prism
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 two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three horizontal rectangles joined one on top of another. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is marked with 3 question marks. The width of the middle rectangle is 24 units. The middle rectangle has a triangle adjoining its left side. The other two sides of the adjoining triangle measure 25 units for the hypotenuse and 7 units for the base. An unmarked triangle adjoins the right side of the bottom rectangle.
The surface area of the triangular prism shown is 5,768 square units. Other dimensions are also shown on the net. What is the height of the prism?
(1 point)
Responses
34.3 units
34.3 units
84 units
, 84 units
100 units
100 units
2,400 units
, , 2,400 units
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 rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the 3 rectangles is 1 centimeter. The length of the outer rectangles is 2.5 centimeters. The length of the middle rectangle is 3 centimeters. Two right triangles adjoin the middle rectangle on the top and bottom along the 3 centimeter side, with their perpendicular height measuring 2 centimeters. A right angle is shown where the perpendicular height intersects with the triangle base.
What is the surface area of the triangular prism whose net is shown?
(1 point)
Responses
8 cm2
, 8 cm squared
2.48 cm2
, , 2.48 cm squared
6 cm2
, 6 cm squared
14 cm2
14 cm squared
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heres the answers to the test:3
1.C
2.C
3.A
4.A
5.D
might be mixed up for yall...
i hope you get 100%:3
To find the surface area of the triangular prism, we need to find the area of each of the 3 parallelograms and the area of the 2 triangles.
1. The area of each parallelogram can be found by multiplying the width (4 cm) by the length (12 cm). So, each parallelogram has an area of 4 cm * 12 cm = 48 cm².
2. The triangular prism has 3 parallelograms, so the total area of the parallelograms is 3 * 48 cm² = 144 cm².
3. The area of the triangle can be found by using the formula: Area = 1/2 * base * height. In this case, the base of the triangle is 12 cm and the height is 9 cm. So, the area of each triangle is 1/2 * 12 cm * 9 cm = 54 cm².
4. The triangular prism has 2 triangles, so the total area of the triangles is 2 * 54 cm² = 108 cm².
5. To find the surface area, we add the area of the parallelograms and the area of the triangles: 144 cm² + 108 cm² = 252 cm².
Therefore, the surface area of the triangular prism whose net is shown is 252 cm².
To find the surface area of a triangular prism, we need to first calculate the areas of each face and then add them up.
In this case, the triangular prism consists of three parallelograms and two triangles.
Let's calculate the areas of each face:
1. The middle parallelogram:
The width of the parallelogram is given as 4 centimeters, and the length is given as 12 centimeters.
To find the area, we multiply the width by the length: 4 cm * 12 cm = 48 cm².
2. The top and bottom triangles:
The triangles have a base of 12 centimeters and a height of 9 centimeters.
To find the area, we use the formula for the area of a triangle: (1/2) * base * height.
For each triangle: (1/2) * 12 cm * 9 cm = 54 cm².
So the total surface area is the sum of the areas of all the faces:
48 cm² + 54 cm² + 54 cm² = 156 cm².
Therefore, the correct answer is 156 cm².
Explanation:
To find the surface area of the triangular prism, we need to find the area of each of the three rectangles and the area of each of the two triangles.
The area of each rectangle is 1 cm (width) times either 2.5 cm or 3 cm (length), so they both have an area of:
1 cm × 2.5 cm = 2.5 cm2
1 cm × 3 cm = 3 cm2
The two triangles are congruent, so we can find the area of one and multiply by 2. The formula for the area of a triangle is 1/2 times base times height, which gives us:
1/2 × 3 cm × 2 cm = 3 cm2
So the total area of the two triangles is:
2 × 3 cm2 = 6 cm2
Now we just need to add up the area of the three rectangles and the two triangles:
2.5 cm2 + 3 cm2 + 2.5 cm2 + 6 cm2 = 14 cm2
Therefore, the surface area of the triangular prism is 14 cm2.
So the correct answer is:
14 cm2
Explanation:
To find the height of the prism, we need to use the formula for the surface area of a triangular prism, which is:
Surface Area = 2 × base area + lateral area
The base area is the area of the rectangle, which is:
base × height = 24 units × height
The lateral area is the sum of the areas of the two triangles. The area of the triangle with hypotenuse 25 units and base 7 units can be found using the Pythagorean theorem:
height² + (7/2)² = (25/2)²
Simplifying this equation gives:
height² + 24.5² = 625/4
height² = 625/4 - 24.5²
height² ≈ 550.25
height ≈ 23.45 units (rounded to two decimal places)
The area of this triangle is:
1/2 × 7 units × height ≈ 81.79 square units
The other triangle has the same area, so the total lateral area is:
2 × 81.79 square units = 163.58 square units
Now we can plug in all the values into the formula for surface area and solve for height:
5,768 square units = 2(24 units × height) + 163.58 square units
5,768 square units - 163.58 square units = 48 units × height
5,604.42 square units = 48 units × height
height ≈ 117.17 units (rounded to two decimal places)
Therefore, the height of the prism is approximately 117.17 units.
So the correct answer is:
117.17 units