Question: William used eight identical parallelograms to make a design on a square poster board with a side length of 44 cm. Each parallelogram has a base of 7 cm and a height of 8 cm, as shown.
What is the area of William’s poster board that is not covered by the eight identical parallelograms?
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cm²
1. **State the problem:** We need to find the area of the square poster board that is not covered by the eight identical parallelograms.
2. **Given data:**
- Side length of square poster board: $44$ cm
- Number of parallelograms: $8$
- Base of each parallelogram: $7$ cm
- Height of each parallelogram: $8$ cm
3. **Formula for area of square:**
$$\text{Area}_{square} = \text{side}^2$$
4. **Formula for area of parallelogram:**
$$\text{Area}_{parallelogram} = \text{base} \times \text{height}$$
5. **Calculate area of the square:**
$$\text{Area}_{square} = 44^2 = 1936 \text{ cm}^2$$
6. **Calculate area of one parallelogram:**
$$\text{Area}_{parallelogram} = 7 \times 8 = 56 \text{ cm}^2$$
7. **Calculate total area covered by 8 parallelograms:**
$$8 \times 56 = 448 \text{ cm}^2$$
8. **Calculate uncovered area:**
$$\text{Uncovered area} = \text{Area}_{square} - \text{Area covered} = 1936 - 448 = 1488 \text{ cm}^2$$
**Final answer:** The area of the poster board not covered by the parallelograms is $1488$ cm².