Step-by-step explanation:
To find the area of each shape, we'll use the formulas for the area of a trapezoid, a rhombus, and a triangle.
1. **Trapezoid (Shape B)**:
Area = \( \frac{1}{2} \times ( \text{sum of parallel sides} ) \times \text{height} \)
Given:
- Bottom parallel side = 5 cm
- Top parallel side = 2.5 cm
- Height = 2 cm
Substituting the values:
Area = \( \frac{1}{2} \times (5 + 2.5) \times 2 \)
Area = \( \frac{1}{2} \times 7.5 \times 2 \)
Area = \( 3.75 \, \text{cm}^2 \)
2. **Rhombus (Shape C)**:
Area = \( \text{base} \times \text{height} \)
Given:
- Base = 2.5 cm
- Height = 2 cm
Substituting the values:
Area = \( 2.5 \times 2 \)
Area = \( 5 \, \text{cm}^2 \)
3. **Triangle (Shape D)**:
Area = \( \frac{1}{2} \times \text{base} \times \text{height} \)
Given:
- Base = 2.5 cm
- Height = 2.2 cm
Substituting the values:
Area = \( \frac{1}{2} \times 2.5 \times 2.2 \)
Area = \( 2.75 \, \text{cm}^2 \)
So, the areas of Manuel's shapes are:
- Trapezoid (Shape B): 3.75 square centimeters
- Rhombus (Shape C): 5 square centimeters
- Triangle (Shape D): 2.75 square centimeters
