Question

Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over? The triangles have a base of 4cm and a height of 6cm. The rectangles measure 12cm by 7cm, 12cm by 4cm, 12cm by 7cm

(1 point)
Responses

324 cm2
324 cm squared

240 cm2
240 cm squared

184 cm2
184 cm squared

84 cm2
84 cm squared
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Answer 1

To find out how much fabric will be left over after making the tent, we first need to calculate the total area of the fabric Jordan purchased, and then calculate the area of the tent she is going to make.

### Step 1: Calculate the area of the purchased fabric
The fabric is a square with sides of 18 cm:
\[
\text{Area of fabric} = \text{side} \times \text{side} = 18 \, \text{cm} \times 18 \, \text{cm} = 324 \, \text{cm}^2
\]

### Step 2: Calculate the area of the tent

**Area of the triangular bases:**
The tent has two triangular bases, each with a base of 4 cm and a height of 6 cm:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{cm} \times 6 \, \text{cm} = 12 \, \text{cm}^2
\]
Since there are two triangles:
\[
\text{Total area of triangles} = 2 \times 12 \, \text{cm}^2 = 24 \, \text{cm}^2
\]

**Area of the rectangular sides:**
There are three rectangles:
1. Rectangle 1: 12 cm by 7 cm
\[
\text{Area} = 12 \, \text{cm} \times 7 \, \text{cm} = 84 \, \text{cm}^2
\]
2. Rectangle 2: 12 cm by 4 cm
\[
\text{Area} = 12 \, \text{cm} \times 4 \, \text{cm} = 48 \, \text{cm}^2
\]
3. Rectangle 3: 12 cm by 7 cm
\[
\text{Area} = 12 \, \text{cm} \times 7 \, \text{cm} = 84 \, \text{cm}^2
\]

Now, we sum the areas of the rectangles:
\[
\text{Total area of rectangles} = 84 \, \text{cm}^2 + 48 \, \text{cm}^2 + 84 \, \text{cm}^2 = 216 \, \text{cm}^2
\]

### Step 3: Total area of the tent
Now, combining the areas of the triangular bases and the rectangular sides:
\[
\text{Total area of tent} = \text{Area of triangles} + \text{Area of rectangles} = 24 \, \text{cm}^2 + 216 \, \text{cm}^2 = 240 \, \text{cm}^2
\]

### Step 4: Calculate the leftover fabric
Now subtract the area of the tent from the area of the fabric:
\[
\text{Leftover fabric} = \text{Area of fabric} - \text{Total area of tent} = 324 \, \text{cm}^2 - 240 \, \text{cm}^2 = 84 \, \text{cm}^2
\]

Thus, the amount of fabric left over is \( \boxed{84 \, \text{cm}^2} \).