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
30 square centimeters
30 square centimeters
33 square centimeters
33 square centimeters
39 square centimeters
39 square centimeters
To find the total area of the piece of jewelry, we need to calculate the area of each individual shape and then add them together.
1. Area of rectangle = length x width = 9 cm x 3 cm = 27 square cm
2. Area of each triangle = (base x height) / 2 = (2 cm x 3 cm) / 2 = 3 square cm (for one triangle, multiply by 2 to account for 2 triangles)
3. Total area = area of rectangle + 2 x area of triangle = 27 square cm + 2 x 3 square cm = 27 square cm + 6 square cm = 33 square cm
Therefore, the total area of the piece of jewelry is 33 square centimeters. The correct answer 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?(1 point)
feet
To find the length in feet of the side of the supply closet labeled with the question mark, we need to first calculate the area of the original composite shape (before the rectangular area marked 8 feet in length is removed).
1. Area of rectangular shape = length x width = (8 ft + ? ft) x (3 ft + 2 ft) = (8 ft + ? ft) x 5 ft
Given that the total area of the whole design (including the part that was removed) is 36 square feet, we know that:
36 sq ft = Area of original shape (8 ft + ? ft) x 5 ft + area of removed rectangular area (8 ft x unknown width)
Since the total area is 36 square feet, we can set up the following equation:
36 = (8 + ?) x 5 + 8 x ?
Now, let's solve for the side labeled with the question mark:
36 = 40 + 5? + 8?
36 = 40 + 13?
-4 = 13?
? = -4 / 13
? = -0.3077 feet
Therefore, the length in feet of the side of the supply closet labeled with the question mark is approximately -0.308 feet.
explain
Apologies for the mistake in the previous explanation. Let's correct that.
Given:
- Total area of the whole design (including the part that was removed) is 36 square feet.
- The original composite shape consists of a rectangle with the following measurements:
- The length along the right side = 2 feet.
- The width along the left side = 3 feet.
- The width of the removed rectangle = unknown.
We need to find the length in feet of the side of the supply closet labeled with the question mark.
Let the width of the removed rectangle be "x" feet.
The total area of the original composite shape can be calculated as follows:
Original area = (2 feet + x feet) * 3 feet
According to the given information, the total area of the original design (before the 8 ft x x rectangular area was removed) is 36 square feet. Therefore:
(2 + x) * 3 = 36
6 + 3x = 36
3x = 30
x = 10 feet
Therefore, the width of the removed rectangle is 10 feet.
Now, to find the length in feet of the side labeled with the question mark in the supply closet:
2 + x = 2 + 10 = 12 feet
So, the length in feet of the side of the supply closet labeled with the question mark is 12 feet.
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
6 units
6 units
0.5 units
0.5 units
316 units
Start Fraction 3 over 16 End Fraction units
1.5 units
First, let's simplify the given ratio x/8 = y/16.
To find the value of x when y is 3 units:
We can set up the proportion using the simplified ratio:
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 when y is 3 units is 1.5 units.
The correct answer is 1.5 units.
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?(1 point)
Responses
To create a smaller-scale drawing of the original printed photograph, Li would need to reduce the dimensions proportionally. This means all dimensions need to be scaled down by the same factor.
If Li chooses dimensions that are smaller than 6 inches by 4 inches, she would be reducing the size of the image.
For example:
- 3 inches by 2 inches would be a smaller scale drawing of the original printed photograph because all dimensions have been halved.
Therefore, 3 inches by 2 inches represents a smaller scale drawing of the original printed photograph.
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?(1 point)
Responses
2 inches by 1 inch
2 inches by 1 inch
1.5 inches by 1 inch
1.5 inches by 1 inch
12 inches by 8 inches
12 inches by 8 inches
1 inch by 0.5 inches