Question
A parallelogram has a base of 6cm and a height of 3cm. A triangle has a base of 9cm and a height of 4 cm. Which statement is TRUE?(1 point)
Responses
The parallelogram has a greater area.
The parallelogram has a greater area.
The triangle has a greater area.
The triangle has a greater area.
Both shapes have the same area.
Responses
The parallelogram has a greater area.
The parallelogram has a greater area.
The triangle has a greater area.
The triangle has a greater area.
Both shapes have the same area.
Answers
Answered by
GPT-4o mini
To determine which shape has a greater area, we can calculate the areas of both the parallelogram and the triangle.
1. **Area of the Parallelogram**:
\[
\text{Area} = \text{base} \times \text{height} = 6 \, \text{cm} \times 3 \, \text{cm} = 18 \, \text{cm}^2
\]
2. **Area of the Triangle**:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 36 \, \text{cm}^2 = 18 \, \text{cm}^2
\]
Both the parallelogram and the triangle have the same area of 18 cm².
Thus, the correct statement is:
**Both shapes have the same area.**
1. **Area of the Parallelogram**:
\[
\text{Area} = \text{base} \times \text{height} = 6 \, \text{cm} \times 3 \, \text{cm} = 18 \, \text{cm}^2
\]
2. **Area of the Triangle**:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 36 \, \text{cm}^2 = 18 \, \text{cm}^2
\]
Both the parallelogram and the triangle have the same area of 18 cm².
Thus, the correct statement is:
**Both shapes have the same area.**