A landscape architect planned a flower garden in the shape of a parallelogram. If the
base and height are multiplied by to create a new parallelogram, what is the new
area? Round to the nearest unit, if necessary.

Question

A landscape architect planned a flower garden in the shape of a parallelogram. If the
base and height are multiplied by

to create a new parallelogram, what is the new
area? Round to the nearest unit, if necessary.

UpStudy AI · Accepted Answer

To determine the new area of the parallelogram after scaling both the base and height by $$ \frac{1}{2} $$, let's break it down step by step.

### Original Area
The area $$ A $$ of a parallelogram is calculated using the formula:
$$
A = \text{base} \times \text{height} \quad \text{or} \quad A = b \times h
$$

### Scaling the Base and Height
If both the base $$ b $$ and the height $$ h $$ are multiplied by $$ \frac{1}{2} $$, their new values become:
$$
\text{New base} = \frac{1}{2}b
$$
$$
\text{New height} = \frac{1}{2}h
$$

### New Area Calculation
The new area $$ A' $$ of the parallelogram with the scaled dimensions is:
$$
A' = \left( \frac{1}{2}b \right) \times \left( \frac{1}{2}h \right) = \frac{1}{4} (b \times h) = \frac{1}{4}A
$$

### Conclusion
The new area is **one fourth** of the original area.

**Example:**
- **Original Area**: Suppose the original area was $$ 80 $$ square units.
- **New Area**: $$ \frac{1}{4} \times 80 = 20 $$ square units.

Since no specific numerical values were provided in your question, the general answer is:

**The new area is one fourth of the original area.**
The new area is one fourth of the original area.

A landscape architect planned a flower garden in the shape of a parallelogram. If the
base and height are multiplied by to create a new parallelogram, what is the new
area? Round to the nearest unit, if necessary.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Original Area

Scaling the Base and Height

New Area Calculation

Conclusion

The Deep Dive

preguntas relacionadas

Latest Geometry Questions

A landscape architect planned a flower garden in the shape of a parallelogram. If the base and height are multiplied by to create a new parallelogram, what is the new area? Round to the nearest unit, if necessary.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Original Area

Scaling the Base and Height

New Area Calculation

Conclusion

The Deep Dive

preguntas relacionadas

Latest Geometry Questions

A landscape architect planned a flower garden in the shape of a parallelogram. If the
base and height are multiplied by to create a new parallelogram, what is the new
area? Round to the nearest unit, if necessary.