Consider the cube shown below. Identify the two-dimensional shape of the cross-section if the cube is sliced horizontally.
Starting with the same cube, identify the two-dimensional shape of the cross-section if the cube is sliced vertically.
Explain why the shapes are the same or different.
If the cube is sliced horizontally, the two-dimensional shape of the cross-section is a square.
If the cube is sliced vertically, the two-dimensional shape of the cross-section is also a square.
The shapes are the same because no matter which direction the cube is sliced, the cross-section will always be perpendicular to the edges of the cube and will thus always be a square. The orientation of the square may be different depending on the direction of the slice, but it is still a square. Therefore, the shape of the cross-section does not depend on the direction of the slice.
Use the image to answer the question.
A composite shape is drawn using a rectangle and 2 triangles. A horizontally aligned rectangle is 9 centimeters long and 3 centimeters wide. A right triangle facing upward adjoins the rectangle on the left side marked 3 centimeters. A right triangle facing downward adjoins the rectangle on the right side. The base leg of both triangles measures 2 centimeters.
Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?
Responses
39 square centimeters
39 square centimeters
30 square centimeters
30 square centimeters
27 square centimeters
27 square centimeters
33 square centimeters
33 square centimeters
Be sure to use the formula 12bh for the area of each triangle.
The area of the rectangle is (length x width) = (9 cm x 3 cm) = 27 square cm.
The area of each triangle is 1/2(base x height) = 1/2(2 cm x 3 cm) = 3 square cm.
Since there are two triangles, the total area of both triangles is 2 x 3 square cm = 6 square cm.
To find the total area of the composite shape, we add the area of the rectangle and the area of the triangles.
Total area = area of rectangle + area of triangles
Total area = 27 square cm + 6 square cm
Total area = 33 square cm
Therefore, the total area of the piece of jewelry is 33 square centimeters.
The correct response is:
33 square centimeters
make it shorter
The total area of the composite shape made of a rectangle and two triangles is 33 square centimeters.
explain how but make it short
Add the area of the rectangle and the two triangles to get the total area, which is 33 square centimeters.
Use the image to answer the question.
A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side is 3 feet. Corners are marked with right angles.
Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark?
To find the length of the side labeled with a question mark, we need to first find the area of the original horizontally aligned rectangle.
The area of a rectangle is length x width.
We know that the remaining length on the right side is 2 feet, and the remaining width on the left side is 3 feet.
So, the area of the original rectangle is 2 feet x 3 feet = 6 square feet.
We also know that an 8 feet x unknown width rectangular area is removed, so the area of the removed rectangular area is 8 feet x unknown width = 8u.
The total area of the composite shape is then 6 square feet - 8u + 36 square feet.
Simplifying this expression, we get:
6 - 8u + 36 = 42
-8u + 42 = 42
-8u = 0
u = 0
Therefore, the width of the removed section is 0 feet, meaning no section was removed. So, the original width remains the same, and the length of the side labeled with a question mark is also 8 feet.
Therefore, the length of the side labeled with a question mark is 8 feet.
To identify the two-dimensional shape of the cross-section of the cube when it is sliced horizontally, we need to visualize the cube and picture a horizontal cut through it.
Start by imagining a cube, which is a three-dimensional object with six square faces and 12 edges. When we slice the cube horizontally, we are essentially cutting it parallel to the base in a straight line.
By examining the cube, we can deduce that a horizontal slice will result in a two-dimensional shape that is a square. This is because the horizontal cut passes through the entire width and height of the cube, thus intersecting all four sides of the square faces.
Now, let's consider the two-dimensional shape of the cross-section when the cube is sliced vertically. In this case, we are visualizing a straight, vertical cut through the cube.
Again, by examining the cube, we can conclude that a vertical slice will yield a two-dimensional shape that is also a square. This is because the vertical cut passes through the entire length and height of the cube, intersecting all four sides of the square faces.
To explain why the shapes are the same for both the horizontal and vertical cuts, we can look at the symmetry of the cube. In a cube, all of the square faces are congruent to each other, meaning they have the same size and shape. Therefore, regardless of the orientation of the cut (horizontal or vertical), the resulting cross-section will always be a square. The only difference is the orientation of the square within the cross-section; it may appear as a diamond shape (if viewed diagonally) in one cut and as a rectangle (if viewed from any side) in the other cut, but it is still a square.
In summary, when the cube is sliced horizontally or vertically, the resulting two-dimensional shape of the cross-section is a square, as each slice intersects all four sides of the square faces. The shapes are the same because of the congruence and symmetry of the cube's square faces.