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?
(1 point)
Responses
27 square centimeters
27 square centimeters
33 square centimeters
33 square centimeters
39 square centimeters
39 square centimeters
30 square centimeters
The total area of the piece of jewelry can be calculated by finding the area of each of the shapes (rectangle and two triangles) separately and then adding them together.
Rectangle area = length * width = 9 cm * 3 cm = 27 square cm
Triangle area = (base * height) / 2
Triangle on the left:
Area = (3 cm * 3 cm) / 2 = 4.5 square cm
Triangle on the right:
Area = (2 cm * 3 cm) / 2 = 3 square cm
Total area = Rectangle area + Triangle area + Triangle area
Total area = 27 square cm + 4.5 square cm + 3 square cm = 34.5 square cm
The total area is 34.5 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?(1 point)
feet
To find the length of the side labeled with a question mark, we need to calculate the area of the original rectangle and then find the width of the rectangle from the given areas and lengths.
Total Area = Original Rectangle Area - Removed Rectangle Area
Given:
Original rectangle length (unknown) * original rectangle width (unknown) = Original rectangle area = ? square feet
Remaining rectangle length = 2 feet
Remaining rectangle width = 3 feet
Removed Rectangle Area = 8 feet * ? = 8 * ? square feet
Original rectangle area = (unknown) * (unknown) square feet
Given that the total area is 36 square feet:
36 = (unknown) * (unknown) square feet - 8 * ? square feet
To find the values of the unknown, we need to solve this equation. However, without the specific values provided in the scenario or a numerical equation, the exact length of the side labeled with a question mark cannot be determined solely with the information provided.
Ethan writes the ratio x8=y16 to help him reduce the size of a two-dimensional shape. If the new value of y is 3 units, what will be the value of x ?(1 point)
Responses
0.5 units
0.5 units
1.5 units
1.5 units
316 units
Start Fraction 3 over 16 End Fraction units
6 units
To solve for the value of x, given that y = 3 units and the ratio x:8 = y:16, we can set up a proportion to find the value of x.
x/8 = 3/16
Cross-multiply to solve for x:
16x = 8*3
16x = 24
x = 24/16
x = 1.5 units
Therefore, the value of x is 1.5 units.