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Area and Volume Unit Test 8 of 158 of 15 Items Question Use the image to answer the question. An illustration shows an outline...Asked by goofy ah bugger
Area and Volume Unit Test
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Question
Use the image to answer the question.
An illustration shows an outline of a right arrow consisting of a rectangle and a triangular head to its right. The length of the rectangle is 4 and the width is 2. The right width of the triangle does not show a line. It forms the central part of the verticle base of the triangle. The other parts of the base are labeled 2 on the top and bottom each. The perpendicular height from the base to the top vertex of the triangle is labeled as 5.
An artist is planning to paint an arrow using the pattern shown. What is the amount of area in square feet that will be painted?
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Answered by
GPT-4o
To determine the total area that will be painted, we need to calculate the area of the rectangle and the area of the triangle separately and then add them together.
**Step 1: Calculate the area of the rectangle.**
The rectangle's dimensions are given as:
- Length = 4 feet
- Width = 2 feet
The area of a rectangle is calculated using the formula:
\[ \text{Area}_{rectangle} = \text{length} \times \text{width} \]
Substitute the given values:
\[ \text{Area}_{rectangle} = 4 \, \text{feet} \times 2 \, \text{feet} = 8 \, \text{square feet} \]
**Step 2: Calculate the area of the triangle.**
The triangle's base includes the width of the rectangle's right side plus two segments each of length 2 feet:
- Base = 2 feet (left segment) + 2 feet (center segment) + 2 feet (right segment) = 6 feet
- Height = 5 feet
The area of a triangle is calculated using the formula:
\[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
Substitute the given values:
\[ \text{Area}_{triangle} = \frac{1}{2} \times 6 \, \text{feet} \times 5 \, \text{feet} = \frac{1}{2} \times 30 \, \text{square feet} = 15 \, \text{square feet} \]
**Step 3: Add the areas of the rectangle and the triangle to find the total area.**
\[ \text{Total area} = \text{Area}_{rectangle} + \text{Area}_{triangle} = 8 \, \text{square feet} + 15 \, \text{square feet} = 23 \, \text{square feet} \]
So, the amount of area that will be painted is:
\[ 23 \, \text{square feet} \]
**Step 1: Calculate the area of the rectangle.**
The rectangle's dimensions are given as:
- Length = 4 feet
- Width = 2 feet
The area of a rectangle is calculated using the formula:
\[ \text{Area}_{rectangle} = \text{length} \times \text{width} \]
Substitute the given values:
\[ \text{Area}_{rectangle} = 4 \, \text{feet} \times 2 \, \text{feet} = 8 \, \text{square feet} \]
**Step 2: Calculate the area of the triangle.**
The triangle's base includes the width of the rectangle's right side plus two segments each of length 2 feet:
- Base = 2 feet (left segment) + 2 feet (center segment) + 2 feet (right segment) = 6 feet
- Height = 5 feet
The area of a triangle is calculated using the formula:
\[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
Substitute the given values:
\[ \text{Area}_{triangle} = \frac{1}{2} \times 6 \, \text{feet} \times 5 \, \text{feet} = \frac{1}{2} \times 30 \, \text{square feet} = 15 \, \text{square feet} \]
**Step 3: Add the areas of the rectangle and the triangle to find the total area.**
\[ \text{Total area} = \text{Area}_{rectangle} + \text{Area}_{triangle} = 8 \, \text{square feet} + 15 \, \text{square feet} = 23 \, \text{square feet} \]
So, the amount of area that will be painted is:
\[ 23 \, \text{square feet} \]
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