Use the image described 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?
31 square miles
28 square miles
25 square miles
21 square miles
To find the area of the composite figure, we need to calculate the area of each individual rectangle first and then add them up.
Area of the original rectangle:
Length = 7 miles, Width = 3 miles
Area = Length x Width = 7 miles x 3 miles = 21 square miles
Area of the left side rectangle extension:
Length = 6 miles, Width = 3 miles
Area = Length x Width = 6 miles x 3 miles = 18 square miles
Area of the right side rectangle extension:
Length = 1 mile, Width = 1 mile
Area = Length x Width = 1 mile x 1 mile = 1 square mile
Total area = 21 square miles + 18 square miles + 1 square mile = 40 square miles
Therefore, the area of the composite figure is 40 square miles.
choose an answer from the responses
The correct answer is not included in the responses provided. The closest option to the correct answer of 40 square miles is 31 square miles.
Use the image described 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?
30 square miles
33 square miles
27 square miles
39 square miles
To find the total area of the piece of jewelry, we need to calculate the area of each individual shape (rectangle and two triangles) and then add them together.
Area of the rectangle:
Length = 9 cm, Width = 3 cm
Area = Length x Width = 9 cm x 3 cm = 27 square cm
Area of the triangle facing upward:
Base = 2 cm, Height = 3 cm (the same as the width of the rectangle)
Area = 0.5 x Base x Height = 0.5 x 2 cm x 3 cm = 3 square cm
Area of the triangle facing downward:
Base = 2 cm, Height = 3 cm (the same as the width of the rectangle)
Area = 0.5 x Base x Height = 0.5 x 2 cm x 3 cm = 3 square cm
Total area = Area of rectangle + Area of triangle facing upward + Area of triangle facing downward
Total area = 27 square cm + 3 square cm + 3 square cm
Total area = 33 square cm
Therefore, the total area of the piece of jewelry is 33 square centimeters.
Given that the options provided are in square miles, we need to convert square centimeters to square miles. However, the provided options do not include 33 square miles, so none of the provided options are correct.
Use the image described 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?
30 square centimeters
33 square centimeters
27 square centimeters
39 square centimeters
To find the total area of the jewelry piece, we need to calculate the area of each individual component (rectangle and two triangles).
Area of the rectangle:
Length = 9 cm, Width = 3 cm
Area = Length x Width = 9 cm x 3 cm = 27 square cm
Area of the triangle facing upwards:
Base = 2 cm, Height = 3 cm (the same height as the rectangle)
Area = 0.5 x Base x Height = 0.5 x 2 cm x 3 cm = 3 square cm
Area of the triangle facing downwards:
Base = 2 cm, Height = 3 cm
Area = 0.5 x Base x Height = 0.5 x 2 cm x 3 cm = 3 square cm
Total area = Area of rectangle + Area of triangle facing upwards + Area of triangle facing downwards
Total area = 27 square cm + 3 square cm + 3 square cm
Total area = 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?
__ feet
To find the width of the side of the supply closet labeled with a question mark, we start by calculating the area of the original rectangle and then subtracting the area of the removed rectangle to find the remaining area.
Area of the original rectangle:
Length = 2 feet + 8 feet + Question mark feet
Width = 3 feet
Area = Length x Width = (2 + 8 + Question mark) feet x 3 feet = 30 feet x 3 feet = 90 square feet
Area of the removed rectangle:
Length = 8 feet
Width = 8 feet
Area = Length x Width = 8 feet x 8 feet = 64 square feet
Remaining area (after removing the rectangle) = Total area - Area of removed rectangle
Remaining area = 90 square feet - 64 square feet = 26 square feet
Now, we know that the total area of the supply closet is 36 square feet, and the remaining area is 26 square feet, meaning the removed rectangle's area plus the unknown area gives 36 square feet. Therefore, the unknown area (the side labeled with the question mark) must have an area of 10 square feet.
We can calculate the width (labeled by the question mark) by dividing the area by the length:
Width = Area / Length = 10 square feet / 2 feet = 5 feet
Therefore, the side of the supply closet labeled with the question mark is 5 feet in length.