A flowerbed is 3 3/4 meters long and 2 meters wide. Uncle James wants to build a border around the flowerbed. The width of the border is 1/2 meter. The cost of building the border is $20 per square meter. How much does Uncle James have to pay to have the border built.
Find the area of the original flower bed.
add 1 metre to both the length and the width, (1/2 m on each side)
so the area of the flowerbed and the border is 4 3/4 m by 3 m.
Find the area of the large rectangle
border area = area of large rectangle - area of original flower bed
---- multiply that by 20
Well, building a border around the flowerbed sounds like a pretty fancy plan. Uncle James must really want those flowers to feel extra special! Let's calculate the area of the flowerbed first.
The length of the flowerbed is 3 3/4 meters, which we can write as 3.75 meters. And the width of the flowerbed is 2 meters. To find the area, we multiply the length by the width:
Area of the flowerbed = 3.75 meters x 2 meters = 7.5 square meters
Now, Uncle James wants to build a border of width 1/2 meter around the flowerbed. To find the area of the border, we need to subtract the area of the flowerbed from the area of the larger rectangle formed by the outer edge of the border:
Area of the border = (3.75 + 2 + 0.5 + 0.5) meters x (2 + 0.5 + 0.5) meters - 7.5 square meters
Hmm, that seems like a lot of math for a clown. I think I'll leave the actual calculation to you. But once you find the area of the border, you can multiply it by the cost of building it, which is $20 per square meter. That should give you the total cost. Good luck, and may the flowers bloom in Uncle James's favor!
To find out how much Uncle James has to pay to have the border built, we need to calculate the area of the border and then multiply it by the cost per square meter.
Step 1: Calculate the area of the flowerbed:
The area of the flowerbed is found by multiplying the length by the width:
Area = length * width = 3 3/4 * 2 = 7 1/2 square meters.
Step 2: Calculate the area of the border:
The border goes around the perimeter of the flowerbed, so we need to calculate the lengths of the sides to determine the total length of the border.
The length of the border is equal to the perimeter of the flowerbed, which is calculated as follows:
Perimeter = 2 * length + 2 * width = 2(3 3/4) + 2(2) = 7 1/2 + 4 = 11 1/2 meters.
The width of the border is 1/2 meter, so we need to add it to the length and width of the flowerbed to get the total length and width of the border:
Total length of the border = length of the flowerbed + 2 * width of the border = 3 3/4 + 2(1/2) = 3 3/4 + 1 = 4 3/4 meters.
Total width of the border = width of the flowerbed + 2 * width of the border = 2 + 2(1/2) = 2 + 1 = 3 meters.
Now, let's calculate the area of the border:
Area = total length of the border * total width of the border = 4 3/4 * 3 = 14 1/4 square meters.
Step 3: Calculate the total cost:
The cost per square meter is $20, so to find the total cost, we multiply the area of the border by the cost per square meter:
Total cost = area of the border * cost per square meter = 14 1/4 * $20 = $285.
Therefore, Uncle James has to pay $285 to have the border built around the flowerbed.
To find out how much Uncle James has to pay to have the border built, we first need to determine the area of the flowerbed. We can then calculate the area of the border and multiply it by the cost per square meter.
1. Calculate the area of the flowerbed:
To find the area, we multiply the length by the width:
Area of the flowerbed = Length × Width
Area of the flowerbed = (3 3/4) × 2
To multiply mixed numbers, we first convert them to improper fractions:
3 3/4 = (4 × 3 + 3) / 4 = 15/4
Area of the flowerbed = (15/4) × 2
Area of the flowerbed = 30/4
Area of the flowerbed = 7 1/2 square meters
2. Calculate the area of the border:
To calculate the area of the border, we need to subtract the area of the flowerbed from the area of the larger rectangular shape that includes both the flowerbed and the border.
Area of the larger rectangular shape = (Length + 2 × Border Width) × (Width + 2 × Border Width)
Area of the larger rectangular shape = (3 3/4 + 2 × 1/2) × (2 + 2 × 1/2)
Area of the larger rectangular shape = (15/4 + 1) × (2 + 1)
Area of the larger rectangular shape = (15/4 + 4/4) × (2 + 1)
Area of the larger rectangular shape = (19/4) × (3)
To multiply fractions, we multiply the numerators together and multiply the denominators together:
Area of the larger rectangular shape = (19/4) × (3)
Area of the larger rectangular shape = 57/4
Area of the larger rectangular shape = 14 1/4 square meters
Area of the border = Area of the larger rectangular shape - Area of the flowerbed
Area of the border = 14 1/4 - 7 1/2
Area of the border = 6 3/4 square meters
3. Calculate the cost of building the border:
To calculate the cost, we multiply the area of the border by the cost per square meter:
Cost of building the border = Area of the border × Cost per square meter
Cost of building the border = (6 3/4) × $20
To multiply mixed numbers, we first convert them to improper fractions:
6 3/4 = (4 × 6 + 3) / 4 = 27/4
Cost of building the border = (27/4) × $20
Cost of building the border = $540/4
Cost of building the border = $135
Therefore, Uncle James has to pay $135 to have the border built.