Question: Find the area of the shape. Show your work o
16 cm
14 cm
23 cm
19 cm
34 cm
Graph shape: a composite polygon made of a top parallelogram-like section attached to a bottom trapezoid-like section, with a dashed 14 cm perpendicular height across the top section and a dashed 19 cm perpendicular height down to the bottom base; position_hint: center
What is the area of this shape?
1. **State the problem:** We need to find the area of a composite polygon consisting of a top parallelogram-like section and a bottom trapezoid-like section.
2. **Identify the shapes and dimensions:**
- Top section is a parallelogram with base $16$ cm and height $14$ cm.
- Bottom section is a trapezoid with bases $23$ cm and $34$ cm, and height $19$ cm.
3. **Formulas:**
- Area of a parallelogram: $$\text{Area} = \text{base} \times \text{height}$$
- Area of a trapezoid: $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$
4. **Calculate the area of the top parallelogram:**
$$\text{Area}_{\text{top}} = 16 \times 14 = 224 \text{ cm}^2$$
5. **Calculate the area of the bottom trapezoid:**
$$\text{Area}_{\text{bottom}} = \frac{(23 + 34)}{2} \times 19$$
Show intermediate step with cancellation:
$$\text{Area}_{\text{bottom}} = \frac{\cancel{(23 + 34)}}{2} \times 19 = \frac{57}{2} \times 19$$
Calculate:
$$= 28.5 \times 19 = 541.5 \text{ cm}^2$$
6. **Calculate total area:**
$$\text{Area}_{\text{total}} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 224 + 541.5 = 765.5 \text{ cm}^2$$
**Final answer:** The area of the composite shape is $$\boxed{765.5 \text{ cm}^2}$$.