Question
An illustration shows rectangle extending to a triangle on the right. The top of the rectangle extends as the hypotenuse toward the bottom. The dimensions of the figure are as follows: the top is 8 centimeters, the left is 4 centimeters, and the bottom is 10 centimeters, including the side of the extended triangle.
What is the area of the figure in square centimeters?(1 point)
What is the area of the figure in square centimeters?(1 point)
Answers
Answered by
GPT-4o mini
To find the area of the given figure, which consists of a rectangle and a right triangle, we can break it down into two parts - the area of the rectangle and the area of the triangle.
1. **Area of the Rectangle:**
The dimensions of the rectangle are given as follows:
- Width (top) = 8 cm
- Height (left) = 4 cm
The area of the rectangle can be calculated using the formula:
\[
\text{Area of rectangle} = \text{width} \times \text{height} = 8 \, \text{cm} \times 4 \, \text{cm} = 32 \, \text{cm}^2
\]
2. **Finding the dimensions of the Triangle:**
The bottom of the figure, which may not specifically refer to the triangle, is given as 10 cm. However, we need to clarify the dimensions of the triangle. Since the problem states that the rectangle extends to form a triangle, we can assume the triangle is right-angled at its base.
The base of the triangle is the difference between the rectangle's top width and its bottom width:
\[
\text{Base of triangle} = 10 \, \text{cm} - 8 \, \text{cm} = 2 \, \text{cm}
\]
The height of the triangle corresponds with the height of the rectangle, which is 4 cm.
Thus:
- Base of triangle = 2 cm
- Height of triangle = 4 cm
The area of the triangle can be calculated using the formula:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \, \text{cm} \times 4 \, \text{cm} = 4 \, \text{cm}^2
\]
3. **Total Area:**
Now we can add the areas of the rectangle and the triangle to find the total area of the figure:
\[
\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle} = 32 \, \text{cm}^2 + 4 \, \text{cm}^2 = 36 \, \text{cm}^2
\]
Thus, the total area of the figure is \( \boxed{36} \) square centimeters.
1. **Area of the Rectangle:**
The dimensions of the rectangle are given as follows:
- Width (top) = 8 cm
- Height (left) = 4 cm
The area of the rectangle can be calculated using the formula:
\[
\text{Area of rectangle} = \text{width} \times \text{height} = 8 \, \text{cm} \times 4 \, \text{cm} = 32 \, \text{cm}^2
\]
2. **Finding the dimensions of the Triangle:**
The bottom of the figure, which may not specifically refer to the triangle, is given as 10 cm. However, we need to clarify the dimensions of the triangle. Since the problem states that the rectangle extends to form a triangle, we can assume the triangle is right-angled at its base.
The base of the triangle is the difference between the rectangle's top width and its bottom width:
\[
\text{Base of triangle} = 10 \, \text{cm} - 8 \, \text{cm} = 2 \, \text{cm}
\]
The height of the triangle corresponds with the height of the rectangle, which is 4 cm.
Thus:
- Base of triangle = 2 cm
- Height of triangle = 4 cm
The area of the triangle can be calculated using the formula:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \, \text{cm} \times 4 \, \text{cm} = 4 \, \text{cm}^2
\]
3. **Total Area:**
Now we can add the areas of the rectangle and the triangle to find the total area of the figure:
\[
\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle} = 32 \, \text{cm}^2 + 4 \, \text{cm}^2 = 36 \, \text{cm}^2
\]
Thus, the total area of the figure is \( \boxed{36} \) square centimeters.
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