Question
The parks department has started building a new playground at Canyonside Park. The shape of the playground is shown below.
A playground is made up of a rectangle and a triangle. The rectangle has a base of 36 feet and a height of 10 feet. The triangle has a base of 36 feet and a height of 14 feet.
The supervisor needs to purchase wood chips to cover the ground in the playground area. If wood chips are sold in bags containing enough to cover 4 square feet and these bags cost $8.00 apiece, how much will it cost to cover the entire area of the playground with wood chips?
$612.00
$1,224.00
$1,728.00
$4,896.00
A playground is made up of a rectangle and a triangle. The rectangle has a base of 36 feet and a height of 10 feet. The triangle has a base of 36 feet and a height of 14 feet.
The supervisor needs to purchase wood chips to cover the ground in the playground area. If wood chips are sold in bags containing enough to cover 4 square feet and these bags cost $8.00 apiece, how much will it cost to cover the entire area of the playground with wood chips?
$612.00
$1,224.00
$1,728.00
$4,896.00
Answers
Answered by
GPT-4o mini
To find the total cost to cover the playground with wood chips, we first need to determine the area of both the rectangle and the triangle that comprise the playground.
1. **Calculate the area of the rectangle:**
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height} = 36 \, \text{feet} \times 10 \, \text{feet} = 360 \, \text{square feet}
\]
2. **Calculate the area of the triangle:**
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 36 \, \text{feet} \times 14 \, \text{feet} = \frac{1}{2} \times 504 = 252 \, \text{square feet}
\]
3. **Total area of the playground:**
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 360 \, \text{square feet} + 252 \, \text{square feet} = 612 \, \text{square feet}
\]
4. **Determine how many bags of wood chips are needed:**
Each bag covers 4 square feet, so the number of bags required is:
\[
\text{Number of bags} = \frac{\text{Total Area}}{\text{Area per bag}} = \frac{612 \, \text{square feet}}{4 \, \text{square feet per bag}} = 153 \, \text{bags}
\]
5. **Calculate the total cost:**
Each bag costs $8.00, therefore the total cost is:
\[
\text{Total Cost} = \text{Number of bags} \times \text{Cost per bag} = 153 \times 8 = 1224
\]
Thus, the total cost to cover the entire area of the playground with wood chips is \(\$1,224.00\).
The answer is:
\[
\boxed{1,224.00}
\]
1. **Calculate the area of the rectangle:**
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height} = 36 \, \text{feet} \times 10 \, \text{feet} = 360 \, \text{square feet}
\]
2. **Calculate the area of the triangle:**
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 36 \, \text{feet} \times 14 \, \text{feet} = \frac{1}{2} \times 504 = 252 \, \text{square feet}
\]
3. **Total area of the playground:**
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 360 \, \text{square feet} + 252 \, \text{square feet} = 612 \, \text{square feet}
\]
4. **Determine how many bags of wood chips are needed:**
Each bag covers 4 square feet, so the number of bags required is:
\[
\text{Number of bags} = \frac{\text{Total Area}}{\text{Area per bag}} = \frac{612 \, \text{square feet}}{4 \, \text{square feet per bag}} = 153 \, \text{bags}
\]
5. **Calculate the total cost:**
Each bag costs $8.00, therefore the total cost is:
\[
\text{Total Cost} = \text{Number of bags} \times \text{Cost per bag} = 153 \times 8 = 1224
\]
Thus, the total cost to cover the entire area of the playground with wood chips is \(\$1,224.00\).
The answer is:
\[
\boxed{1,224.00}
\]