Coordinate Geometry and Nets Unit Test
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Question
Use the image to answer the question.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB?(1 point)
The surface area of the rectangular prism can be calculated by adding the areas of all the six rectangles. The areas are:
- First rectangle: 54 square inches
- Second rectangle: 24 square inches
- Third rectangle: 36 square inches
- Fourth rectangle: 24 square inches (since it's similar to the second rectangle)
- Fifth rectangle: 54 square inches (since it's similar to the third rectangle)
- Sixth rectangle: 54 square inches (since it's similar to the first rectangle)
Adding all those areas together, we get:
54 + 24 + 36 + 24 + 54 + 54 = 246
Therefore, the surface area of the rectangular prism is 246 square inches.
The length of AB is 6 inches.
Coordinate Geometry and Nets Unit Test
9 of 159 of 15 Items
Question
Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and bigger. The second and fourth are similar and smaller. The area of the second rectangle is labeled 24 square inches. The third rectangle shares the top and bottom sides with two similar rectangles, one on each side. The area of the top rectangle is labeled as 54 square inches and the area of the third rectangle is labeled as 36 square inches.
What is the surface area of the rectangular prism?
(1 point)
You are drawing a net that shows a rectangular prism with an area of 52 square feet. If two of the rectangles in the net are 4 ft.×3 ft., what is the value of the third measurement you need to know to have an area of 52 square feet?(1 point)
We know the area of the rectangular prism is 52 square feet, and we know that two of the rectangles in the net are 4 ft. x 3 ft.
To find the missing dimension, we can use the formula for the area of a rectangle:
Area = length x width
We know that the area of each of the 4 ft. x 3 ft. rectangles is:
4 ft. x 3 ft. = 12 square feet
Since there are two of these rectangles, their combined area is:
12 square feet + 12 square feet = 24 square feet
To find the area of the rest of the rectangular prism, we can subtract this from the total area:
52 square feet - 24 square feet = 28 square feet
So the missing dimension should have an area of 28 square feet. We can use the formula for the area of a rectangle again to find its dimensions:
Area = length x width
28 square feet = length x width
We don't have enough information to find the exact dimensions, but we can list some possible combinations of length and width that would work:
- 7 ft. x 4 ft.
- 14 ft. x 2 ft.
- 28 ft. x 1 ft.
Any of those combinations would give a rectangular prism with an area of 52 square feet, where two of the rectangles are 4 ft. x 3 ft.
How does the net of a fish tank with no lid compare to the net of a fish tank with its lid on?(1 point)
Responses
The net of the fish tank with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with no lid comprises six rectangles, three pairs of congruent rectangles.
The net of the fish tank with a lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with no lid comprises six rectangles, three pairs of congruent rectangles.
Both the nets are identical.
Both the nets are identical.
The net of the fish tank with no lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with its lid comprises six rectangles, three pairs of congruent rectangles.
The net of the fish tank with no lid comprises five rectangles, two pairs of congruent rectangles and one odd rectangle, whereas the net of the fish tank with its lid comprises six rectangles, three pairs of congruent rectangles.
The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
The net of the fish tank with no lid has four rectangular faces, two pairs of congruent rectangles, and the net of the fish tank with its lid has six rectangular faces, three pairs of congruent rectangles.
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)
To calculate the surface area of the triangular prism, we need to find the areas of all the faces and then add them up.
The net consists of three vertical rectangles. The base and top rectangles have dimensions of 7 mm x 8 mm each, so their area is:
7 mm x 8 mm = 56 mm²
The middle rectangle is a bit different because it's connected to the two triangles on each side. Each triangle has a base of 7 mm (the width of the rectangle) and a height of 6 mm. Using the Pythagorean theorem, we can find that the hypotenuse (the side connecting the two triangles across the rectangle) has a length of 10 mm. So the area of each triangle is:
(1/2) x base x height = (1/2) x 7 mm x 6 mm = 21 mm²
The area of the middle rectangle is simply:
8 mm x 7 mm = 56 mm²
To find the total surface area, we can add up all the areas:
56 mm² + 56 mm² + 21 mm² + 21 mm² + 56 mm² + 56 mm² = 266 mm²
Therefore, the surface area of the triangular prism is 266 mm².
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)
To find the surface area of the triangular prism, we need to find the areas of all six faces.
1. The base triangle has a base of 17 cm and a height of 9 cm, so its area is:
(1/2) x base x height = (1/2) x 17 cm x 9 cm = 76.5 cm²
2. There is another triangle opposite to the base with a vertical height of 7.8 cm and a base of 9 cm, so its area is:
(1/2) x base x height = (1/2) x 9 cm x 7.8 cm = 35.1 cm²
3. The two rectangular faces have dimensions of 9 cm x 17 cm, so each of their areas is:
9 cm x 17 cm = 153 cm²
4. Finally, we have two more triangular faces connecting the base triangle and the rectangular faces. These are congruent triangles with a base of 17 cm, a height of 9 cm, and a slant height of 7.8 cm. We can find the area of one of these triangles using the formula:
Area = (1/2) x base x height
= (1/2) x 17 cm x 9 cm
= 76.5 cm²
So the total area of both triangles is:
2 x 76.5 cm² = 153 cm²
To find the total surface area, we can add up all six areas:
76.5 cm² + 35.1 cm² + 2(153 cm²) = 528.6 cm²
Therefore, the total surface area of the triangular prism is 528.6 square centimeters, rounded to two decimal places.
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.
To find the total surface area of the sawhorse, we need to find the area of each of its six faces and then add them up.
Let's start with the two rectangular sides. Each side has dimensions of 39 inches (height) by 19 inches (width), so the area of one side is:
39 in x 19 in = 741 in²
Since there are two of these sides, their combined area is:
2 x 741 in² = 1482 in²
Next, we can find the area of the top and bottom faces, which are also rectangles with dimensions of 27 inches (length) by 19 inches (width). So the area of one of these faces is:
27 in x 19 in = 513 in²
Since there are two of these faces, their combined area is:
2 x 513 in² = 1026 in²
Finally, we need to find the area of the two triangular ends of the sawhorse. Each end is an isosceles triangle with legs of 19 inches and height of 39 inches. We can use the Pythagorean theorem to find the length of the base (the third side) of each triangle:
a² + b² = c²
where a = b = 19 inches and c = 40.14 inches (the hypotenuse)
19² + 19² = 40.14²
722 = 1612.6596
c ≈ 40.14 inches
So each triangle has an area of:
(1/2) x base x height = (1/2) x 19 in x 39 in = 370.5 in²
Since there are two of these triangles, their combined area is:
2 x 370.5 in² = 741 in²
Now we can add up the areas of all six faces:
1482 in² + 1026 in² + 741 in² = 3249 in²
Therefore, the total surface area of the sawhorse is 3249 square inches, rounded to the nearest hundredth.