Question
The area on the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?
8cm is the base, across the top is indented and up and labeled 3 cm then right 4 cm then down on the right and labeled 2 cm to the right
8cm is the base, across the top is indented and up and labeled 3 cm then right 4 cm then down on the right and labeled 2 cm to the right
Answers
GPT-4o mini
To find the height of the larger rectangle in the described composite figure, we first need to analyze the shape based on the provided dimensions.
1. **Understanding the Dimensions**:
- Base of the rectangle = 8 cm (0.8 m, if converting to meters)
- Indented distance upward = 3 cm (0.3 m)
- Horizontal rightward distance = 4 cm (0.4 m)
- Downward distance from the right = 2 cm (0.2 m)
2. **Sketch the Figure**:
- Start with a rectangle that has a base of 8 cm.
- After going up by 3 cm, draw a line to the right for 4 cm.
- Then, draw a line downward for 2 cm.
- This completes creating a composite figure where the top part above the indent is still part of the larger rectangle.
3. **Area of the Composite Figure**:
- The total area of the figure is given as 52 square meters. However, we need to ensure we are using compatible units. So let's convert the dimensions in centimeters to meters:
- Base = 0.8 m
- Heights from the smaller part (3 cm + 2 cm) must be added to find the total height.
4. **Finding Effective Heights**:
- The total height of the larger rectangle includes the vertical distance above the indent to the top of the rectangle, which is 3 cm, plus the remaining height which we'll call \(h\):
\[
\text{Total Height} = 0.3 + h \quad (\text{where } h \text{ is the height of the rectangle below the indentation})
\]
5. **Formulating the Area**:
The area \(A\) of a rectangle is given by \(A = \text{Base} \times \text{Height}\):
\[
52 = 0.8 \times \text{Total Height}
\]
where \(\text{Total Height} = 0.3 + h\).
6. **Solving for h**:
\[
52 = 0.8 \times (0.3 + h)
\]
\[
52 = 0.24 + 0.8h
\]
\[
52 - 0.24 = 0.8h
\]
\[
51.76 = 0.8h
\]
\[
h = \frac{51.76}{0.8} = 64.7 \text{ m}
\]
So, the value in meters of the height of the larger rectangle is \(h \approx 64.7\) meters.
1. **Understanding the Dimensions**:
- Base of the rectangle = 8 cm (0.8 m, if converting to meters)
- Indented distance upward = 3 cm (0.3 m)
- Horizontal rightward distance = 4 cm (0.4 m)
- Downward distance from the right = 2 cm (0.2 m)
2. **Sketch the Figure**:
- Start with a rectangle that has a base of 8 cm.
- After going up by 3 cm, draw a line to the right for 4 cm.
- Then, draw a line downward for 2 cm.
- This completes creating a composite figure where the top part above the indent is still part of the larger rectangle.
3. **Area of the Composite Figure**:
- The total area of the figure is given as 52 square meters. However, we need to ensure we are using compatible units. So let's convert the dimensions in centimeters to meters:
- Base = 0.8 m
- Heights from the smaller part (3 cm + 2 cm) must be added to find the total height.
4. **Finding Effective Heights**:
- The total height of the larger rectangle includes the vertical distance above the indent to the top of the rectangle, which is 3 cm, plus the remaining height which we'll call \(h\):
\[
\text{Total Height} = 0.3 + h \quad (\text{where } h \text{ is the height of the rectangle below the indentation})
\]
5. **Formulating the Area**:
The area \(A\) of a rectangle is given by \(A = \text{Base} \times \text{Height}\):
\[
52 = 0.8 \times \text{Total Height}
\]
where \(\text{Total Height} = 0.3 + h\).
6. **Solving for h**:
\[
52 = 0.8 \times (0.3 + h)
\]
\[
52 = 0.24 + 0.8h
\]
\[
52 - 0.24 = 0.8h
\]
\[
51.76 = 0.8h
\]
\[
h = \frac{51.76}{0.8} = 64.7 \text{ m}
\]
So, the value in meters of the height of the larger rectangle is \(h \approx 64.7\) meters.