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?
To find the area of the figure, we first need to find the missing dimensions.
Since we know the top side is 6 and the bottom side is 6, and the left side is divided into three parts with a width of 2 for the first part, the width of the third part must also be 2. Therefore, the middle part must be 8 - 2 - 2 = 4.
Now we can calculate the area of the figure:
Area = (6 + 6) * (4 + 8) / 2
Area = 12 * 12 / 2
Area = 144 / 2
Area = 72
Therefore, the area of the figure is 72.
wrong.
I apologize for that mistake. Let's go through the problem again.
First, calculate the area of the rectangle with dimensions 6 by 8:
Area = 6 * 8 = 48 square units
Next, calculate the area of the missing rectangle on the left side. Its dimensions are 6 units tall (the same as the full rectangle) and 2 units wide:
Area = 6 * 2 = 12 square units
Finally, subtract the area of the missing rectangle from the total area:
Total area = 48 - 12 = 36 square units
Therefore, the area of the figure is 36 square units. Thank you for your patience.
wrong
Apologies for the confusion. Let's try to solve it again.
To find the area of the figure, we need to calculate the areas of each individual shape and then subtract the area of the missing rectangle.
1. Calculate the area of the full rectangle: 6 * 8 = 48 square units
2. Calculate the area of the small rectangle that is missing from the left side: 2 * 6 = 12 square units
Subtract the area of the missing rectangle from the total area:
48 - 12 = 36 square units
Therefore, the correct area of the figure is 36 square units.
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?
The area of the swimming pool can be found by calculating the area of the original rectangle and then subtracting the area of the rectangle that was removed.
1. Calculate the area of the original rectangle:
Area = Length * Width
Area = 8 * 7
Area = 56 square yards
2. Calculate the area of the rectangle that was removed:
Since the remaining width along the bottom right is 3 yards and we know the width of the removed rectangle is 3 yards, the length of the removed rectangle can be found by subtracting the width of the removed rectangle from the total width of the original rectangle.
Length of removed rectangle = 7 - 3 = 4 yards
Area of removed rectangle = Length * Width
Area of removed rectangle = 4 * 3
Area of removed rectangle = 12 square yards
3. Calculate the final area of the swimming pool:
Final area = Area of original rectangle - Area of removed rectangle
Final area = 56 - 12
Final area = 44 square yards
Therefore, the area of the swimming pool is 44 square yards.
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?
To find the height of the rectangle, we first need to find the dimensions of the rectangle.
The area of the composite shape is the sum of the areas of the rectangle and the triangle.
Let the height of the rectangle be h centimeters.
1. Area of the rectangle = Base * Height
Area of the rectangle = 6 * h
2. Area of the triangle = 0.5 * Base * Height
Area of the triangle = 0.5 * 6 * 6
Given that the total area of the composite shape is 78 square centimeters:
Area of rectangle + Area of triangle = 78
6h + 0.5*6*6 = 78
6h + 18 = 78
6h = 78 - 18
6h = 60
h = 60 / 6
h = 10
Therefore, the height of the rectangle is 10 centimeters.
A horizontally aligned rectangle is shown as 10 meters long and 6 meters wide. A rectangular area is removed from the bottom right corner, with the remaining length as 8 meters and remaining width as 4 meters. Right angle marks are shown in the five corners of the composite shape.
Rebekah designs a playing field for a new sport. The playing field is pictured. What is the area of the playing field?
To find the area of the playing field, we first need to calculate the area of the original rectangle and then subtract the area of the rectangle that was removed.
1. Calculate the area of the original rectangle:
Area = Length * Width
Area = 10 * 6
Area = 60 square meters
2. Calculate the area of the rectangle that was removed:
The length of the removed rectangle is the difference between the original length and the remaining length: 10 - 8 = 2 meters
The width of the removed rectangle is the difference between the original width and the remaining width: 6 - 4 = 2 meters
Area of removed rectangle = Length * Width
Area of removed rectangle = 2 * 2
Area of removed rectangle = 4 square meters
3. Calculate the area of the playing field:
Area of playing field = Area of original rectangle - Area of removed rectangle
Area of playing field = 60 - 4
Area of playing field = 56 square meters
Therefore, the area of the playing field is 56 square meters.