What is a two-dimensional representation of a three-dimensional figure?(1 point)
a net
a triangular prism
a triangle
a rectangle
a net
Which of the following describes a valid method for calculating the surface area of a triangular prism?
(1 point)
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five
shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the
area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one
triangle and three times the area of one rectangle.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five
shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
10 wide 10 tall triangle side 8 tall 6 long
Solve for the surface area of the triangular prism.
(1 point)
260 square centimeters
320 square centimeters
280 square centimeters
180 square centimeters
To solve for the surface area of the triangular prism, we need to calculate the area of each of the faces and then sum them up.
Given that the triangular prism has a triangular base that is 10 units wide and 10 units tall, and the other face is a rectangle that is 8 units tall and 6 units long.
1. Area of the triangular base = (1/2) * base * height = (1/2) * 10 * 10 = 50 square units
2. Area of the rectangle face = length * width = 8 * 6 = 48 square units
3. There are two triangular bases and three rectangular faces, so the total surface area = 2(triangular base area) + 3(rectangle face area)
4. Total surface area = 2(50) + 3(48) = 100 + 144 = 244 square units
Therefore, the surface area of the triangular prism is 244 square centimeters.
16 wide 11 long 15 tall 17 tall triangle side
What is the surface area of the net of the triangular prism?
(1 point)
779 square meters
790 square meters
822 square meters
768 square meters
To determine the surface area of the net of the triangular prism, we need to calculate the area of each face and then sum them up.
Given the dimensions:
- The triangular base has one side that is 16 units wide and 11 units long.
- The other face is a rectangle that is 15 units tall and 17 units wide (matching the corresponding sides of the triangle).
1. Area of the triangular base:
Area = (1/2) * base * height = (1/2) * 16 * 11 = 88 square units
2. Area of the rectangle face:
Area = height * width = 15 * 17 = 255 square units
3. Since there are two triangular bases and one rectangular face on the net, we calculate the total surface area as follows:
Total surface area = 2(triangular base area) + 1(rectangle face area)
Total surface area = 2(88) + 255 = 176 + 255 = 431 square units
Therefore, the surface area of the net of the triangular prism is 431 square units.
triangle dementions are 17, 15, 16, 11
What is the surface area of the net of the triangular prism?
(1 point)
779 square meters
790 square meters
822 square meters
768 square meters
To find the surface area of the net of the triangular prism, we first need to calculate the area of each face and then sum them up.
Given the dimensions of the triangular prism as 17, 15, 16, 11:
The triangle with sides of length 17, 15, and 16 is a right triangle with sides 8, 15, and 17 (via Pythagorean theorem). Therefore, the base and height of the triangle would be 15 and 8 respectively.
1. Area of the triangle face:
Area = (1/2) * base * height = (1/2) * 15 * 8 = 60 square units
The other face is a rectangle corresponding to the remaining side lengths, 17 and 11:
2. Area of the rectangular face:
Area = length * width = 17 * 11 = 187 square units
Since there are two triangular faces and one rectangular face in the net:
Total surface area = 2(triangle area) + 1(rectangle area)
Total surface area = 2(60) + 187 = 120 + 187 = 307 square units
Therefore, the surface area of the net of the triangular prism is 307 square units.
779 square meters
790 square meters
822 square meters
768 square meters
are the options