To find the total area of Annika's design, we need to calculate the individual areas of the rectangle, the triangle, and the square, and then add them together.
Rectangle:
Length = 12 feet
Width = 4 feet
Area = Length x Width
Area = 12 feet x 4 feet
Area = 48 square feet
Triangle:
Base = 4 feet
Height = 4 feet
Area = (Base x Height) / 2
Area = (4 feet x 4 feet) / 2
Area = 8 square feet
Square:
Side length = 4 feet
Area = Side length x Side length
Area = 4 feet x 4 feet
Area = 16 square feet
Total area of Annika's design:
48 square feet (rectangle) + 8 square feet (triangle) + 16 square feet (square) = 72 square feet
Therefore, Annika's design has an area of 72 square feet.
Use the image described to answer the question.
A composite shape is made up of a rectangle, triangle, and square. A horizontally aligned rectangle has a length of 12 feet and width of 4 feet. A right triangle adjoins the rectangle on the right side, with the vertical side common to the rectangle. A square with a side of 4 feet adjoins the right triangle along the bottom. Right angle marks are located in the four corners of the rectangle and the square, and also in the triangle where the base and vertical side meet.
Annika designs a hole for a miniature golf course. What is the area of Annika’s design in square feet?
? square feet
11 answers
Use the image described to answer the question.
A composite shape is drawn. The vertical width on the left side from top to bottom shows no measurement. The shape is drawn with straight lines and right angles. A horizontal line marked 4 miles is drawn from the upper left corner. A vertical line marked 2 miles drops down from the the top horizontal line. A horizontal line marked 2 miles continues to the right. A vertical line marked 2 miles drops down to become the right edge of the shape. A horizontal line of unknown length is drawn leftward. A vertical line marked 2 miles drops down to the base. A baseline marked 2 miles meets the width side to form the lower left corner.
A city map is shown. What is the area of the city in square miles?
? square miles
A composite shape is drawn. The vertical width on the left side from top to bottom shows no measurement. The shape is drawn with straight lines and right angles. A horizontal line marked 4 miles is drawn from the upper left corner. A vertical line marked 2 miles drops down from the the top horizontal line. A horizontal line marked 2 miles continues to the right. A vertical line marked 2 miles drops down to become the right edge of the shape. A horizontal line of unknown length is drawn leftward. A vertical line marked 2 miles drops down to the base. A baseline marked 2 miles meets the width side to form the lower left corner.
A city map is shown. What is the area of the city in square miles?
? square miles
To determine the area of the city shown on the map, we need to calculate the total area by breaking it down into recognizable shapes.
From the description provided, we can identify the shapes as follows:
1. A rectangle with dimensions of 4 miles by 2 miles (upper part).
Area = Length x Width = 4 miles x 2 miles = 8 square miles
2. A square with side length of 2 miles (right side).
Area = Side length x Side length = 2 miles x 2 miles = 4 square miles
3. A rectangle with unknown horizontal length and vertical length of 6 miles (left side and bottom).
We need to know the length of the unknown horizontal line to calculate this area.
To determine the total area of the city, we need to find the length of the unknown horizontal line. Once we have that measurement, we can calculate the area of the third rectangle and then add up the areas of all three shapes to find the total area of the city. Please provide the length of the unknown horizontal line to complete the calculation.
From the description provided, we can identify the shapes as follows:
1. A rectangle with dimensions of 4 miles by 2 miles (upper part).
Area = Length x Width = 4 miles x 2 miles = 8 square miles
2. A square with side length of 2 miles (right side).
Area = Side length x Side length = 2 miles x 2 miles = 4 square miles
3. A rectangle with unknown horizontal length and vertical length of 6 miles (left side and bottom).
We need to know the length of the unknown horizontal line to calculate this area.
To determine the total area of the city, we need to find the length of the unknown horizontal line. Once we have that measurement, we can calculate the area of the third rectangle and then add up the areas of all three shapes to find the total area of the city. Please provide the length of the unknown horizontal line to complete the calculation.
Use the image to answer the question.
An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top
Solve the following problem using what you know about composite figures. What is the area of the figure?
a. 36 square miles
b. 48 square miles
c. 24 square miles
d. 30 square miles
An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top
Solve the following problem using what you know about composite figures. What is the area of the figure?
a. 36 square miles
b. 48 square miles
c. 24 square miles
d. 30 square miles
To find the area of the figure, we need to break it down into recognizable shapes and calculate the area of each shape.
From the description provided, we have a polygon with the following dimensions:
- Top side: 6 units
- Right side: 8 units
- Bottom side: 6 units
- Left side divided into three parts with a vertical width of 2 units from the top
1. The main shape of the figure (excluding the smaller rectangular piece) is a rectangle with dimensions 6 units by 8 units.
Area of the main rectangle = Length x Width = 6 units x 8 units = 48 square units
2. The smaller rectangular piece missing from the left side can be calculated separately. Given that the left side is divided into three parts and the vertical width is 2 units from the top:
Area of the missing rectangular piece = 6 units x 2 units = 12 square units
To find the total area of the figure, we subtract the area of the missing rectangular piece from the area of the main rectangle:
Total area = Area of main rectangle - Area of missing piece
Total area = 48 square units - 12 square units
Total area = 36 square units
Therefore, the area of the figure is 36 square units, so the correct answer is:
a. 36 square miles.
From the description provided, we have a polygon with the following dimensions:
- Top side: 6 units
- Right side: 8 units
- Bottom side: 6 units
- Left side divided into three parts with a vertical width of 2 units from the top
1. The main shape of the figure (excluding the smaller rectangular piece) is a rectangle with dimensions 6 units by 8 units.
Area of the main rectangle = Length x Width = 6 units x 8 units = 48 square units
2. The smaller rectangular piece missing from the left side can be calculated separately. Given that the left side is divided into three parts and the vertical width is 2 units from the top:
Area of the missing rectangular piece = 6 units x 2 units = 12 square units
To find the total area of the figure, we subtract the area of the missing rectangular piece from the area of the main rectangle:
Total area = Area of main rectangle - Area of missing piece
Total area = 48 square units - 12 square units
Total area = 36 square units
Therefore, the area of the figure is 36 square units, so the correct answer is:
a. 36 square miles.
Use the image to answer the question
A composite figure is comprised of a rectangle and two congruent right triangle on either side. The triangle have a height of 4 inches and a width of 3 inches.
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
28 square inches
16 square inches
7 square inches
34 square inches
A composite figure is comprised of a rectangle and two congruent right triangle on either side. The triangle have a height of 4 inches and a width of 3 inches.
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
28 square inches
16 square inches
7 square inches
34 square inches
Let's break down the information given:
1. The composite figure consists of a rectangle and two congruent right triangles.
2. The right triangles have a height of 4 inches and a base (width) of 3 inches each.
3. The total area of the composite figure is 40 square inches.
To find the area of the rectangle within the composite shape, we need to calculate the area of the right triangles first.
Each right triangle has an area of:
Area of triangle = (base x height) / 2
Area of triangle = (3 inches x 4 inches) / 2
Area of triangle = 12 square inches / 2
Area of triangle = 6 square inches
Since there are two congruent triangles, the total area of both triangles combined is:
Total area of both triangles = 2 x 6 square inches = 12 square inches
Given that the total area of the composite shape is 40 square inches, and 12 square inches are accounted for by the triangles, the remaining area must be the area of the rectangle:
Area of rectangle = Total area - Area of triangles
Area of rectangle = 40 square inches - 12 square inches
Area of rectangle = 28 square inches
Therefore, the area of the rectangle within the composite shape is 28 square inches. So the correct answer is:
28 square inches.
1. The composite figure consists of a rectangle and two congruent right triangles.
2. The right triangles have a height of 4 inches and a base (width) of 3 inches each.
3. The total area of the composite figure is 40 square inches.
To find the area of the rectangle within the composite shape, we need to calculate the area of the right triangles first.
Each right triangle has an area of:
Area of triangle = (base x height) / 2
Area of triangle = (3 inches x 4 inches) / 2
Area of triangle = 12 square inches / 2
Area of triangle = 6 square inches
Since there are two congruent triangles, the total area of both triangles combined is:
Total area of both triangles = 2 x 6 square inches = 12 square inches
Given that the total area of the composite shape is 40 square inches, and 12 square inches are accounted for by the triangles, the remaining area must be the area of the rectangle:
Area of rectangle = Total area - Area of triangles
Area of rectangle = 40 square inches - 12 square inches
Area of rectangle = 28 square inches
Therefore, the area of the rectangle within the composite shape is 28 square inches. So the correct answer is:
28 square inches.
use the image to answer the question
A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.
Solve the following problem: A town has a swimming pool shaped as in the diagram. What is the area of the swimming pool in square yards?
30 square inches
44 square inches
56 square inches
65 square inches
A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.
Solve the following problem: A town has a swimming pool shaped as in the diagram. What is the area of the swimming pool in square yards?
30 square inches
44 square inches
56 square inches
65 square inches
To find the area of the swimming pool, we need to calculate the area of the original rectangle and then subtract the area of the smaller rectangle that was removed, leaving us with the remaining area of the pool.
Given:
Original rectangle:
Length = 8 yards
Width = 7 yards
Smaller rectangle (removed):
Width = 3 yards
One side along the bottom of the original rectangle = 3 yards (remaining width at the bottom right)
1. Area of the original rectangle:
Area = Length x Width
Area = 8 yards x 7 yards
Area = 56 square yards
2. Area of the smaller rectangle:
Area = Length x Width
Since the width is given as 3 yards for the removed rectangle, we need to find the length of the smaller rectangle. The smaller rectangle is formed by removing a 3-yard wide section from the original 7-yard width, meaning a 4-yard width remains.
Length = 4 yards
Area of the smaller rectangle = 4 yards x 3 yards = 12 square yards
Now, to find the area of the swimming pool (remaining area after removing the smaller rectangle):
Area of swimming pool = Area of original rectangle - Area of smaller rectangle
Area of swimming pool = 56 square yards - 12 square yards
Area of swimming pool = 44 square yards
Therefore, the area of the swimming pool in square yards is 44 square yards. Hence, the correct answer is:
44 square inches.
Given:
Original rectangle:
Length = 8 yards
Width = 7 yards
Smaller rectangle (removed):
Width = 3 yards
One side along the bottom of the original rectangle = 3 yards (remaining width at the bottom right)
1. Area of the original rectangle:
Area = Length x Width
Area = 8 yards x 7 yards
Area = 56 square yards
2. Area of the smaller rectangle:
Area = Length x Width
Since the width is given as 3 yards for the removed rectangle, we need to find the length of the smaller rectangle. The smaller rectangle is formed by removing a 3-yard wide section from the original 7-yard width, meaning a 4-yard width remains.
Length = 4 yards
Area of the smaller rectangle = 4 yards x 3 yards = 12 square yards
Now, to find the area of the swimming pool (remaining area after removing the smaller rectangle):
Area of swimming pool = Area of original rectangle - Area of smaller rectangle
Area of swimming pool = 56 square yards - 12 square yards
Area of swimming pool = 44 square yards
Therefore, the area of the swimming pool in square yards is 44 square yards. Hence, the correct answer is:
44 square inches.
Use the image to answer the question
A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.
John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?
12 centimeters
8 centimeters
13 centimeters
10 centimeters
A composite shape is drawn using a rectangle and a triangle. The rectangle has a base labeled as 6 centimeters. A triangle showing a perpendicular height of 6 centimeters is stacked on the top side of the rectangle. The base of the triangle and the top of the rectangle have a common side. Right angle symbols are shown on all four corners of the rectangle.
John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?
12 centimeters
8 centimeters
13 centimeters
10 centimeters
To find the height of the rectangle in the composite shape, we first need to determine the individual areas of the rectangle and the triangle and then use the total area to solve for the height.
Given:
Rectangle:
- Base = 6 centimeters
- Height = h (unknown)
Area of rectangle = Base x Height
Triangle:
- Base = 6 centimeters
- Height = 6 centimeters
Area of triangle = (Base x Height) / 2
Total area of the composite shape = 78 square centimeters
Now, we know that the total area is the sum of the areas of the rectangle and the triangle:
78 = (6 x h) + (6 x 6) / 2
Simplify the equation:
78 = 6h + 18
6h = 60
h = 10 centimeters
Therefore, the height of the rectangle in the composite shape is 10 centimeters. So the correct answer is:
10 centimeters.
Given:
Rectangle:
- Base = 6 centimeters
- Height = h (unknown)
Area of rectangle = Base x Height
Triangle:
- Base = 6 centimeters
- Height = 6 centimeters
Area of triangle = (Base x Height) / 2
Total area of the composite shape = 78 square centimeters
Now, we know that the total area is the sum of the areas of the rectangle and the triangle:
78 = (6 x h) + (6 x 6) / 2
Simplify the equation:
78 = 6h + 18
6h = 60
h = 10 centimeters
Therefore, the height of the rectangle in the composite shape is 10 centimeters. So the correct answer is:
10 centimeters.