Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 70 feet. His back yard has a length of 20 feet and a width of 40 feet. How many square feet of sod does Jayden need to purchase?
First, calculate the area of the front yard:
Area of front yard = length x width = 50 ft x 70 ft = 3,500 square feet
Then, calculate the area of half of the back yard (since Jayden only wants to lay sod on half of it):
Area of back yard = (length x width) / 2 = (20 ft x 40 ft) / 2 = 400 square feet
Finally, add the area of the front yard and half of the back yard together to get the total area of sod needed:
Total area of sod = 3,500 square feet + 400 square feet = 3,900 square feet.
Therefore, Jayden needs to purchase 3,900 square feet of sod.
Julie printed out a picture of each of the five members of her favorite band to decorate her bedroom door. Each picture measures 8 inches by 10 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?
Since there are five pictures, we need to find 5 times the area of one picture.
Area of one picture = length x width = 8 inches x 10 inches = 80 square inches
Therefore, the total area covered by the five pictures would be:
Total area = number of pictures × area of one picture
Total area = 5 × 80 square inches = 400 square inches
So, Julie's door will be covered by 400 square inches of pictures.
The rectangle has an area of 128 square inches and a width of 8 inches. Find the perimeter of the rectangle.
To find the length of the rectangle, we need to divide the area by the width:
Length = Area / Width = 128 sq in / 8 in = 16 in
Now that we know the length is 16 inches and the width is 8 inches, we can use the formula for perimeter:
Perimeter = 2 × (Length + Width)
Plugging in the values we found:
Perimeter = 2 × (16 in + 8 in) = 2 × 24 in = 48 in
Therefore, the perimeter of the rectangle is 48 inches.
Joey is creating a rectangular garden. The garden is 9 feet long and 7 feet wide.
Joey calculated he needs
feet of fencing to close in the garden and
square feet of soil to cover the garden.
To find the amount of fencing needed, we need to calculate the perimeter of the rectangular garden.
Perimeter = 2 × (Length + Width) = 2 × (9 ft + 7 ft) = 2 × 16 ft = 32 ft
Therefore, Joey needs 32 feet of fencing to close in the garden.
To find the amount of soil needed, we need to calculate the area of the rectangular garden.
Area = Length × Width = 9 ft × 7 ft = 63 square feet
Therefore, Joey needs 63 square feet of soil to cover the garden.
The total area of the figure is 77 square centimeters. The overall height of the figure is 9 centimeters.
Drag the correct measurements to label the unknown lengths in the figure.
There are different ways to approach this problem, but one possible method is to use the fact that the figure can be split into two smaller rectangles and a triangle, as shown:
```
x 7
┌────┴────┐ ┌─────┴─────┐
| | | |
| x | | 10 |
| | | |
├─────┬───┤ x├────┬────┤
| 5 | h | | x | h |
└─────┴───┘ └────┴────┘
```
The area of the figure can then be expressed as:
Area = 5x + 7h + (1/2) * 10 * h
Since we know that the total area is 77 square centimeters, we can substitute this value and simplify the equation:
77 = 5x + 7h + 5h
77 = 5x + 12h
x = (77 - 12h) / 5
We are also given that the overall height of the figure is 9 centimeters, so we can substitute this value and solve for h:
9 = h + h
h = 4.5
Now we can plug in the value of h and solve for x:
x = (77 - 12h) / 5
x = (77 - 12 * 4.5) / 5
x = 2.7
Therefore, the lengths of the unknown sides are approximately x = 2.7 centimeters and h = 4.5 centimeters.