To find the surface area of the prism, we need to find the area of each of the three rectangles and the two triangles.
1. Rectangle 1: 7 mm by 8 mm
Area = 7 mm * 8 mm = 56 mm^2
2. Rectangle 2: 7 mm by 8 mm
Area = 7 mm * 8 mm = 56 mm^2
3. Rectangle 3: 7 mm by 8 mm
Area = 7 mm * 8 mm = 56 mm^2
4. Triangle 1: (1/2) * base * height
Area = (1/2) * 6 mm * 8 mm = 24 mm^2
5. Triangle 2: (1/2) * base * height
Area = (1/2) * 6 mm * 8 mm = 24 mm^2
Finally, we add up the areas of all the shapes:
56 mm^2 + 56 mm^2 + 56 mm^2 + 24 mm^2 + 24 mm^2 = 216 mm^2
Therefore, the surface area of the prism is 216 mm^2.
Coordinate Geometry and Nets Unit Test
12 of 1512 of 15 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 vertical rectangles joined one on top of the other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the rectangles is 7 millimeters. The length of the middle rectangle is 8 millimeters. Two right triangles adjoin the middle rectangle on the left and the right, with the perpendicular sides measuring 6 millimeters and the hypotenuse measuring 10 millimeters.
Using the net of the prism shown, what is its surface area?
(1 point)
__ mm2
9 answers
Coordinate Geometry and Nets Unit Test
13 of 1513 of 15 Items
Question
Use the image to answer the question.
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as a triangle in the middle attached to a rectangle on each side. The sides of two legs of the triangle are each labeled 9 centimeters. The length and width of the rectangles is 17 centimeters and 9 centimeters respectively. Another triangle of vertical height 7.8 centimeters is attached to one of the rectangles, opposite to the middle triangle.
What is the total surface area represented by this net of a triangular prism? Your answer should have two decimal places.
(1 point)
cm2
13 of 1513 of 15 Items
Question
Use the image to answer the question.
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as a triangle in the middle attached to a rectangle on each side. The sides of two legs of the triangle are each labeled 9 centimeters. The length and width of the rectangles is 17 centimeters and 9 centimeters respectively. Another triangle of vertical height 7.8 centimeters is attached to one of the rectangles, opposite to the middle triangle.
What is the total surface area represented by this net of a triangular prism? Your answer should have two decimal places.
(1 point)
cm2
To find the total surface area of the prism represented by this net, we need to calculate the areas of all the visible shapes - two triangles and three rectangles.
1. Triangle 1: (1/2) * base * height
Area = (1/2) * 9 cm * 7.8 cm = 35.1 cm^2
2. Rectangle 1: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
3. Rectangle 2: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
4. Triangle 2: (1/2) * base * height
Area = (1/2) * 9 cm * 7.8 cm = 35.1 cm^2
5. Rectangle 3: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
Now, add up all these areas:
35.1 cm^2 + 153 cm^2 + 153 cm^2 + 35.1 cm^2 + 153 cm^2 = 529.2 cm^2
Therefore, the total surface area represented by this net of a triangular prism is 529.2 cm^2.
1. Triangle 1: (1/2) * base * height
Area = (1/2) * 9 cm * 7.8 cm = 35.1 cm^2
2. Rectangle 1: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
3. Rectangle 2: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
4. Triangle 2: (1/2) * base * height
Area = (1/2) * 9 cm * 7.8 cm = 35.1 cm^2
5. Rectangle 3: 17 cm by 9 cm
Area = 17 cm * 9 cm = 153 cm^2
Now, add up all these areas:
35.1 cm^2 + 153 cm^2 + 153 cm^2 + 35.1 cm^2 + 153 cm^2 = 529.2 cm^2
Therefore, the total surface area represented by this net of a triangular prism is 529.2 cm^2.
Kym’s sawhorse is 39 inches tall, 27 inches long, and 19 inches wide. Its diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.(1 point)
in.2
in.2
To find the total surface area of the sawhorse, we need to calculate the areas of each of the six faces: two rectangles for the top and bottom, two rectangles for the sides, and two rectangles for the ends.
1. Top and Bottom Rectangles:
Area = 27 inches * 19 inches = 513 square inches (each)
2. Side Rectangles:
Area = 39 inches * 19 inches = 741 square inches (each)
3. End Rectangles:
Area = 27 inches * 39 inches = 1053 square inches (each)
Now, add the areas of all six faces together:
(2 * 513) + (2 * 741) + (2 * 1053) = 1026 + 1482 + 2106 = 4614 square inches
Therefore, the total surface area of Kym's sawhorse is 4614 square inches.
1. Top and Bottom Rectangles:
Area = 27 inches * 19 inches = 513 square inches (each)
2. Side Rectangles:
Area = 39 inches * 19 inches = 741 square inches (each)
3. End Rectangles:
Area = 27 inches * 39 inches = 1053 square inches (each)
Now, add the areas of all six faces together:
(2 * 513) + (2 * 741) + (2 * 1053) = 1026 + 1482 + 2106 = 4614 square inches
Therefore, the total surface area of Kym's sawhorse is 4614 square inches.
Use the image to answer the question.
A coordinate plane shows the x and y axes ranging from negative 6 to 6 in unit increments. Four points are plotted and labeled on the plane. The coordinates of the plotted points and the labels are as follows: left parenthesis 2 comma 1 right parenthesis is labeled as daisies, left parenthesis 5 comma 1 right parenthesis as roses, left parenthesis 5 comma 5 right parenthesis as lilies, and left parenthesis 2 comma 6 right parenthesis as sunflowers.
A map of a flower shop is shown. Each coordinate represents one foot. How far are the roses from the lilies? Explain how you found your answer.
(2 points)
A coordinate plane shows the x and y axes ranging from negative 6 to 6 in unit increments. Four points are plotted and labeled on the plane. The coordinates of the plotted points and the labels are as follows: left parenthesis 2 comma 1 right parenthesis is labeled as daisies, left parenthesis 5 comma 1 right parenthesis as roses, left parenthesis 5 comma 5 right parenthesis as lilies, and left parenthesis 2 comma 6 right parenthesis as sunflowers.
A map of a flower shop is shown. Each coordinate represents one foot. How far are the roses from the lilies? Explain how you found your answer.
(2 points)
To find the distance between the roses and lilies, we can use the distance formula in coordinate geometry. The distance formula is √((x2 - x1)^2 + (y2 - y1)^2).
Given that the coordinates of the roses are (5, 1) and the coordinates of the lilies are (5, 5), we can plug these values into the distance formula:
√((5 - 5)^2 + (1 - 5)^2)
√(0^2 + (-4)^2)
√(0 + 16)
√16
= 4 feet
Therefore, the roses are 4 feet away from the lilies.
Given that the coordinates of the roses are (5, 1) and the coordinates of the lilies are (5, 5), we can plug these values into the distance formula:
√((5 - 5)^2 + (1 - 5)^2)
√(0^2 + (-4)^2)
√(0 + 16)
√16
= 4 feet
Therefore, the roses are 4 feet away from the lilies.
WRITE IT LIKE A 6TH GRADER
To figure out how far the roses are from the lilies, we can use the distance formula in math. The roses are at the spot (5, 1) and the lilies are at (5, 5).
We can calculate the distance using this formula:
Distance = √((5 - 5)^2 + (1 - 5)^2)
When we do the math, it looks like this:
Distance = √(0^2 + (-4)^2)
Distance = √(0 + 16)
Distance = √16
Distance = 4 feet
So, the roses are 4 feet away from the lilies.
We can calculate the distance using this formula:
Distance = √((5 - 5)^2 + (1 - 5)^2)
When we do the math, it looks like this:
Distance = √(0^2 + (-4)^2)
Distance = √(0 + 16)
Distance = √16
Distance = 4 feet
So, the roses are 4 feet away from the lilies.