Use the image to answer the question.
An illustration shows a rectangle extending upward on the top left and top right sides forming two more rectangles of varying width and length. The dimensions are as follows: The bottom of the rectangle is 7 miles. The extended left side is 6 miles. The vertical height of the left side rectangular extension is 3 miles. The vertical and horizontal lengths of the right side rectangular extension is 1 mile each. There are six right angle symbols at the vertices of the polygon.
What is the area of the composite figure?
(1 point)
To find the area of the composite figure, we need to calculate the area of each individual rectangle and then add them together.
1. Area of the original rectangle:
Area = length x width
Area = 7 miles x 3 miles
Area = 21 square miles
2. Area of the left side rectangular extension:
Area = length x width
Area = 6 miles x 3 miles
Area = 18 square miles
3. Area of the right side rectangular extension:
Area = length x width
Area = 1 mile x 1 mile
Area = 1 square mile
Total area of the composite figure:
21 square miles + 18 square miles + 1 square mile = 40 square miles
Therefore, the area of the composite figure is 40 square miles.
Use the image to answer the question.
An illustration shows a rectangle extending upward on the top left and top right sides forming two more rectangles of varying width and length. The dimensions are as follows: The bottom of the rectangle is 7 miles. The extended left side is 6 miles. The vertical height of the left side rectangular extension is 3 miles. The vertical and horizontal lengths of the right side rectangular extension is 1 mile each. There are six right angle symbols at the vertices of the polygon.
What is the area of the composite figure?
(1 point)
Responses
31 square miles
31 square miles
21 square miles
21 square miles
28 square miles
28 square miles
25 square miles
To find the area of the composite figure, we need to calculate the areas of the individual rectangles and then add them together.
1. Area of the original rectangle:
Area = length x width
Area = 7 miles x 3 miles
Area = 21 square miles
2. Area of the left side rectangular extension:
Area = length x width
Area = 6 miles x 3 miles
Area = 18 square miles
3. Area of the right side rectangular extension:
Area = length x width
Area = 1 mile x 1 mile
Area = 1 square mile
Total area of the composite figure:
21 square miles (original rectangle) + 18 square miles (left side extension) + 1 square mile (right side extension) = 40 square miles
Therefore, the correct answer is missing from the options provided. The area of the composite figure is actually 40 square miles, not 31, 28, or 25 square miles.
which one is right
I apologize for the error in my response. Let me correct it. The correct area of the composite figure, as calculated in my previous response, is 40 square miles, not 31, 28, or 25 square miles. Therefore, the correct answer based on the options provided would be:
- 31 square miles (which was not shown in my previous response)
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)
To find the total area of the piece of jewelry, we need to calculate the areas of the individual shapes (rectangle and triangles) and then add them together.
1. Area of the rectangle:
Area = length x width
Area = 9 cm x 3 cm
Area = 27 square cm
2. Area of the left triangle:
Area = 1/2 x base x height
Area = 1/2 x 2 cm x 3 cm
Area = 3 square cm
3. Area of the right triangle:
Area = 1/2 x base x height
Area = 1/2 x 2 cm x 3 cm
Area = 3 square cm
Total area of the piece of jewelry:
27 square cm (rectangle) + 3 square cm (left triangle) + 3 square cm (right triangle) = 33 square cm
Therefore, the total area of the piece of jewelry 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)
To find the length of the side marked with a question mark, we can use the information provided about the total area and the dimensions of the other rectangles.
Let's denote the width of the original rectangle as x (the side marked with a question mark) and the total length of the original rectangle as L.
Given:
- Length of the original rectangle = L
- Width of the original rectangle = x
- Length of the rectangle removed from the bottom left = 8 feet
- Remaining width on the left side = 3 feet
- Remaining length on the right side = 2 feet
- Total area of the composite shape = 36 square feet
First, let's calculate the area of the original rectangle:
Area of the original rectangle = L * x
Since a horizontally aligned rectangular area of 8 feet in length is removed from the bottom left of the original rectangle, the area of this removed rectangle is 8 * 3 = 24 square feet.
Therefore, the area of the remaining part of the original rectangle is:
Area of remaining part = Area of original rectangle - Area of removed rectangle
Area of remaining part = L * x - 24
The remaining length on the right side is 2 feet, and the remaining width on the left side is 3 feet:
Area of remaining part = 2 * 3 = 6 square feet
Given that the total area of the composite shape is 36 square feet:
L * x - 24 + 6 = 36
L * x - 18 = 36
L * x = 54
x = 54 / L
We know that the total area of the composite shape is the original rectangle's area minus the area of the removed rectangle. So, the total area can be expressed in two ways:
1. L * x - 24 + 6 = 36
2. L * x = 36
From these two equations, we can solve for L and x to find the length of the side labeled with a question mark in feet.