1. **Problem Statement:** Calculate the areas of Figure A and Figure B based on the given dimensions and verify the statements about their areas. 2. **Formulas and Rules:** - Area of a rectangle: $$\text{Area} = \text{length} \times \text{height}$$ - Area of a semicircle: $$\text{Area} = \frac{1}{2} \pi r^2$$ - Area of a square: $$\text{Area} = \text{side}^2$$ - Area of a parallelogram: $$\text{Area} = \text{base} \times \text{height}$$ 3. **Calculate Area of Figure A:** - Rectangle dimensions: length = 7 m, height = 4 m - Area of rectangle: $$7 \times 4 = 28 \text{ m}^2$$ - Semicircle radius = half of height = $$\frac{4}{2} = 2 \text{ m}$$ - Area of one semicircle: $$\frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \times 4 = 2\pi \text{ m}^2$$ - Two semicircles combined form a full circle area: $$2 \times 2\pi = 4\pi \text{ m}^2$$ - Total area of Figure A: $$28 + 4\pi \approx 28 + 12.566 = 40.566 \text{ m}^2$$ 4. **Calculate Area of Figure B:** - Decompose into square and parallelogram. - Square side = 3.5 m, area: $$3.5^2 = 12.25 \text{ m}^2$$ - Parallelogram base = 5 m, height = 3.5 m - Area of parallelogram: $$5 \times 3.5 = 17.5 \text{ m}^2$$ - Total area of Figure B: $$12.25 + 17.5 = 29.75 \text{ m}^2$$ 5. **Verify Statements:** - Statement c is correct: Figure B area is 29.75 m². - Difference in areas: $$40.566 - 29.75 = 10.816 \text{ m}^2$$ - Statement d is incorrect since the difference is about 10.82 m², not 45.99 m². **Final answers:** - Area of Figure A: approximately $$40.57 \text{ m}^2$$ - Area of Figure B: $$29.75 \text{ m}^2$$ - Difference: approximately $$10.82 \text{ m}^2$$