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?
To find the area of the composite figure, we first need to calculate the area of each individual rectangle and then add them up.
1. Area of the original rectangle:
Area = base x height
Area = 7 miles x 3 miles
Area = 21 square miles
2. Area of the left side rectangular extension:
Area = base x height
Area = 6 miles x 3 miles
Area = 18 square miles
3. Area of the right side rectangular extension:
Area = base x height
Area = 1 mile x 1 mile
Area = 1 square mile
Adding up the areas of all three rectangles:
Total area = 21 square miles + 18 square miles + 1 square mile
Total area = 40 square miles
Therefore, the area of the composite figure is 40 square miles.
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?
To find the total area of the piece of jewelry, we need to calculate the area of each individual shape - the rectangle and the two triangles, and then add them up.
1. Area of the rectangle:
Area = base x height
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 3 cm x 3 cm
Area = 4.5 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
Adding up the areas of the rectangle and the two triangles:
Total area = 27 square cm + 4.5 square cm + 3 square cm
Total area = 34.5 square cm
Therefore, the total area of the piece of jewelry is 34.5 square cm.
use the image to answer the question
A composite shape is drawn using a rectangle and 2 triangles. the horizontally aligned rectangle in the middle is 9 centimeters long and 3 centimeters wide. A right triangle facing upward on the right side of the rectangle adjoins the rectangle marked 3 centimeters. A right triangle facing downward on the left side is of the rectangle is also 3 centimeters. 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?
The total area of the jewelry can be calculated by finding the individual areas of the rectangle and the two triangles and then adding them up.
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
Adding up the areas of the rectangle and the two triangles:
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 cm.
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 base of the rectangle is 7 miles. The extended height on 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?
To find the area of the composite figure, we need to calculate the area of each individual rectangle and then add them up.
1. Area of the original rectangle:
Area = base x height
Area = 7 miles x 6 miles
Area = 42 square miles
2. Area of the left side rectangular extension:
Area = base x height
Area = 6 miles x 3 miles
Area = 18 square miles
3. Area of the right side rectangular extension:
Area = base x height
Area = 1 mile x 1 mile
Area = 1 square mile
Adding up the areas of all three rectangles:
Total area = 42 square miles + 18 square miles + 1 square mile
Total area = 61 square miles
Therefore, the area of the composite figure is 61 square miles.
actually the 6 miles was 3
Apologies for the mistake. Let's recalculate the area using the correct dimensions:
1. Area of the original rectangle:
Area = base x height
Area = 7 miles x 3 miles
Area = 21 square miles
2. Area of the left side rectangular extension:
Area = base x height
Area = 3 miles x 3 miles
Area = 9 square miles
3. Area of the right side rectangular extension:
Area = base x height
Area = 1 mile x 1 mile
Area = 1 square mile
Adding up the areas of all three rectangles:
Total area = 21 square miles + 9 square miles + 1 square mile
Total area = 31 square miles
Therefore, the correct area of the composite figure is 31 square miles. Thank you for pointing out the correction.
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 on the bottom of the rectangle is marked as 8 feet in length and unknown in width is removed from the bottom right of the original rectangle. The remaining length on the right side is 2 feet. The remaining width on the left side of the rectangle 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 in feet of the side of the supply closet labeled with the question mark, we need to determine the area of the composite shape minus the area of the rectangular area that was removed from the bottom right of the rectangle (8 feet in length and unknown width).
1. Area of the original rectangle:
Let the unknown length be x feet for the right side.
The area of the original rectangle = 8 feet (length) * x feet (width) = 8x square feet
2. Area of the remaining shape after removing the rectangular area:
The width of this new shape is 3 feet, and the length is x - 2 feet.
The area of this new shape = 3 feet (width) * (x - 2) feet (length) = 3x - 6 square feet
Given that the total area of the composite shape is 36 square feet:
8x - (3x - 6) = 36
Solving for x:
8x - 3x + 6 = 36
5x + 6 = 36
5x = 30
x = 6
Therefore, the length in feet of the side of the supply closet labeled with the question mark is 6 feet.
is there a simpler method of solving the problem
Yes, there is a simpler method of solving the problem.
Given that the total area of the composite shape is 36 square feet, and we have removed an 8 feet by 3 feet area from the bottom right of the rectangle, we can find the area of the remaining shape without calculating the exact measurements of the sides.
1. Find the area of the removed rectangular shape:
Area = 8 feet * 3 feet = 24 square feet
2. Subtract the area of the removed shape from the total area to find the area of the remaining shape:
Remaining area = Total area - Removed area
Remaining area = 36 square feet - 24 square feet
Remaining area = 12 square feet
3. The remaining shape is a rectangle with unknown sides. Since the length of the bottom left side is 3 feet, the length of the side labeled with a question mark will be such that when combined with 3 feet, the area is equal to 12 square feet.
Since 3 feet * x feet = 12 square feet,
x = 12 / 3
x = 4
Therefore, the length in feet of the side of the supply closet labeled with the question mark is 4 feet.
Ethan writes the ratio x8=y/16 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)
To find the value of x when y is 3 units in the ratio x/8 = y/16, we can set up a proportion and solve for x.
Given:
x/8 = y/16
Substitute y = 3:
x/8 = 3/16
Cross multiply to solve for x:
16x = 8 * 3
16x = 24
x = 24 / 16
x = 1.5
Therefore, the value of x when y is 3 units in the ratio x/8 = y/16 is 1.5.
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
To create a smaller scale drawing of the original printed photograph, the dimensions of the smaller copies must be proportional to the original dimensions of 6 inches by 4 inches.
You can select dimensions that are a fraction of the original size, for example:
- 3 inches by 2 inches (which is half of the original dimensions)
- 1.5 inches by 1 inch (which is one-quarter of the original dimensions)
These dimensions represent smaller scale drawings of the original printed photograph.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
When creating a scale drawing of a triangle, the ratio of corresponding dimensions will be maintained. In this case, the ratio of the heights of the original triangle to the scale drawing height is equal to the ratio of the bases of the original triangle to the scale drawing base. This is because the triangles are similar.
Given:
Original triangle height = 5 inches
Original triangle base = 8 inches
Scale drawing height = 2 inches
Since the height ratio of the original to the scale drawing is maintained:
5 / 2 = 8 / x
To find x (the scale drawing base), we can cross multiply:
5 * x = 2 * 8
5x = 16
x = 16 / 5
x = 3.2 inches
Now that we have the scale drawing base (3.2 inches) and height (2 inches), we can calculate the area of the scale drawing triangle:
Area = (1/2) * base * height
Area = (1/2) * 3.2 * 2
Area = 3.2 square inches
Therefore, the area of Crystal's scale drawing triangle is 3.2 square inches.
What is the approximate circumference of a circle that has a radius of 90? Use 3.14 for π and express your answer to the tenths place.(1 point)
To find the circumference of a circle, you can use the formula: Circumference = 2 * π * radius.
Given:
Radius = 90 units
π (pi) = 3.14
Substitute the values into the formula:
Circumference = 2 * 3.14 * 90
Circumference = 565.2
Rounded to the nearest tenth, the approximate circumference of the circle with a radius of 90 units is 565.2 units.
What is the approximate circumference of a circle that has a diameter of 379? Use 3.14 for π and express your answer to the hundredths place. (1 point)
To find the circumference of a circle when given the diameter, you can use the formula: Circumference = π * diameter.
Given:
Diameter = 379 units
π (pi) = 3.14
Substitute the values into the formula:
Circumference = 3.14 * 379
Circumference = 1190.66
Rounded to the nearest hundredth, the approximate circumference of the circle with a diameter of 379 units is 1190.66 units.
The approximate circumference of a circle is 7,459 miles. What is the diameter rounded to the nearest hundredths place? Use 3.14 for π .(1 point)
To find the diameter of a circle when given the circumference, you can use the formula: Circumference = π * diameter.
Given:
Circumference = 7,459 miles
π (pi) = 3.14
We are looking for the diameter. Let's solve for it.
Substitute the values into the formula:
7,459 = 3.14 * diameter
To solve for the diameter, divide both sides by 3.14:
diameter = 7,459 / 3.14
diameter ≈ 2375.79617834
Rounded to the nearest hundredth, the diameter is approximately 2375.80 miles.
The radius of a circle is 98 mm. What is the area of the circle? Write your answer to the hundredths place. Use 3.14 for π .(1 point)
To find the area of a circle given the radius, you can use the formula: Area = π * radius^2.
Given:
Radius = 98 mm
π (pi) = 3.14
Substitute the values into the formula:
Area = 3.14 * (98)^2
Area = 3.14 * 9604
Area = 30182.56
Therefore, the area of the circle with a radius of 98 mm is approximately 30182.56 square millimeters.
If the area of a circle is 28.26 cm2 , what is the radius of the circle?(1 point)
To find the radius of a circle given the area, you can use the formula: Area = π * radius^2.
Given:
Area = 28.26 cm²
π (pi) ≈ 3.14
Now we can solve for the radius:
28.26 = 3.14 * radius^2
radius^2 = 28.26 / 3.14
radius^2 ≈ 9
To find the radius, take the square root of both sides:
radius ≈ √9
radius ≈ 3
Therefore, the radius of the circle is approximately 3 cm.
Complete the table by finding the circumference and area of a circle with a radius of 279 inches. Substitute 3.14 for pi. Express your answers to the hundredths place.(1 point)
To find the circumference and area of a circle with a radius of 279 inches, we can use the formulas:
Circumference = 2 * π * radius
Area = π * (radius)^2
Given:
Radius = 279 inches
π (pi) = 3.14
Substitute the radius into the formulas:
Circumference:
Circumference = 2 * 3.14 * 279
Circumference = 1750.68 inches
Area:
Area = 3.14 * (279)^2
Area = 3.14 * 77841
Area = 244489.54 square inches
Therefore, for a circle with a radius of 279 inches, the circumference is approximately 1750.68 inches and the area is approximately 244489.54 square inches.
what is both the circumference and area for the radius, 279?
For a circle with a radius of 279 units:
Circumference = 2 * π * radius
Circumference = 2 * 3.14 * 279
Circumference = 1750.68 units
Area = π * radius^2
Area = 3.14 * 279^2
Area = 3.14 * 77841
Area = 244489.54 square units
Therefore, for a circle with a radius of 279 units, the circumference is approximately 1750.68 units and the area is approximately 244489.54 square units.
A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia’s scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work.(4 points)
To find the area of Magnolia's scale drawing, we need to first determine the actual area of the original triangular flag using the given dimensions, and then use the scale factor to calculate the area of the scale drawing.
Given:
Original triangular flag: Height = 15 inches, Base = 25 inches
Scale drawing: New Base = 10 inches
1. Calculate the actual area of the original triangular flag:
Area = (1/2) * base * height
Area = (1/2) * 25 * 15
Area = 187.5 square inches
2. Determine the scale factor for the base:
Scale factor = New Base / Original Base
Scale factor = 10 / 25
Scale factor = 0.4
3. Use the scale factor to calculate the height of the scale drawing:
New Height = Scale factor * Original Height
New Height = 0.4 * 15
New Height = 6 inches
4. Calculate the area of Magnolia's scale drawing using the new dimensions:
Area of the scale drawing = (1/2) * New Base * New Height
Area of the scale drawing = (1/2) * 10 * 6
Area of the scale drawing = 30 square inches
Therefore, the area of Magnolia's scale drawing is 30 square inches.