Question
find the area of the figure. Round yoru answer to the nearest hundredth if required
one arrow with sides of 1in, 4in, 1in, 5in, 10in, 5in
one arrow with sides of 1in, 4in, 1in, 5in, 10in, 5in
Answers
Answered by
GPT-4o mini
To find the area of the arrow shape from the given dimensions, let's first visualize the arrow. It consists of a rectangle and a triangle.
1. **Identify components**:
- The main body of the arrow can be thought of as a rectangle with a width of 1 inch and a height of 10 inches.
- The arrowhead is made up of two triangles. Each triangle has a base of 4 inches and a height depending on the given dimensions.
2. **Calculating the area of the rectangle**:
The area of the rectangle \( A_{\text{rectangle}} \) is calculated as:
\[
A_{\text{rectangle}} = \text{width} \times \text{height} = 1 \text{ in} \times 10 \text{ in} = 10 \text{ in}^2
\]
3. **Calculating the area of the triangles**:
Each triangle has a base of 4 inches, but we need the height.
However, since only the dimensions of the arrow are given, we need to make an assumption here about the configuration of the triangles.
- If we consider the arrowhead to have a height corresponding to the arrow’s shape, we can guess or denote it as 5 inches (this could vary based on actual shapes).
The area of one triangle \( A_{\text{triangle}} \) is calculated as:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
So, if we assume the height of the triangles is 5 inches:
\[
A_{\text{triangle}} = \frac{1}{2} \times 4 \text{ in} \times 5 \text{ in} = 10 \text{ in}^2
\]
Since there are two identical triangles (each forming half of the arrowhead):
\[
A_{\text{total\_triangles}} = 2 \times A_{\text{triangle}} = 2 \times 10 \text{ in}^2 = 20 \text{ in}^2
\]
4. **Calculating total area**:
Now, add the area of the rectangle and the area of the triangles:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{total\_triangles}} = 10 \text{ in}^2 + 20 \text{ in}^2 = 30 \text{ in}^2
\]
Thus, the area of the figure is:
\[
\boxed{30 \text{ in}^2}
\]
1. **Identify components**:
- The main body of the arrow can be thought of as a rectangle with a width of 1 inch and a height of 10 inches.
- The arrowhead is made up of two triangles. Each triangle has a base of 4 inches and a height depending on the given dimensions.
2. **Calculating the area of the rectangle**:
The area of the rectangle \( A_{\text{rectangle}} \) is calculated as:
\[
A_{\text{rectangle}} = \text{width} \times \text{height} = 1 \text{ in} \times 10 \text{ in} = 10 \text{ in}^2
\]
3. **Calculating the area of the triangles**:
Each triangle has a base of 4 inches, but we need the height.
However, since only the dimensions of the arrow are given, we need to make an assumption here about the configuration of the triangles.
- If we consider the arrowhead to have a height corresponding to the arrow’s shape, we can guess or denote it as 5 inches (this could vary based on actual shapes).
The area of one triangle \( A_{\text{triangle}} \) is calculated as:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
So, if we assume the height of the triangles is 5 inches:
\[
A_{\text{triangle}} = \frac{1}{2} \times 4 \text{ in} \times 5 \text{ in} = 10 \text{ in}^2
\]
Since there are two identical triangles (each forming half of the arrowhead):
\[
A_{\text{total\_triangles}} = 2 \times A_{\text{triangle}} = 2 \times 10 \text{ in}^2 = 20 \text{ in}^2
\]
4. **Calculating total area**:
Now, add the area of the rectangle and the area of the triangles:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{total\_triangles}} = 10 \text{ in}^2 + 20 \text{ in}^2 = 30 \text{ in}^2
\]
Thus, the area of the figure is:
\[
\boxed{30 \text{ in}^2}
\]
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