Subjects geometry

Area Composite Figures 2E9342

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem asks to find the area of the given figures, which are squares, rectangles, and composite shapes. 2. The formula for the area of a square is $$A = s^2$$ where $s$ is the side length. 3. The formula for the area of a rectangle is $$A = l \times w$$ where $l$ is length and $w$ is width. 4. For composite figures, break them into simpler shapes (rectangles/squares), find each area, then sum them. 5. Calculate each figure's area: (1) Square with side 7 m: $$A = 7^2 = 49\text{ m}^2$$ (2) Square with side 15 cm: $$A = 15^2 = 225\text{ cm}^2$$ (3) Rectangle 6 cm by 13 cm: $$A = 6 \times 13 = 78\text{ cm}^2$$ (4) Rectangle 18 m by 9 m: $$A = 18 \times 9 = 162\text{ m}^2$$ (5) L-shaped figure: split into two rectangles: - Rectangle 1: 6 cm by 4 cm - Rectangle 2: 8 cm by (10 - 4) cm = 8 cm by 6 cm Calculate areas: $$A_1 = 6 \times 4 = 24\text{ cm}^2$$ $$A_2 = 8 \times 6 = 48\text{ cm}^2$$ Total area: $$A = 24 + 48 = 72\text{ cm}^2$$ (6) Composite step shape: split into two rectangles: - Rectangle 1: 3 cm by 4 cm - Rectangle 2: (12 - 3) cm by 4 cm = 9 cm by 4 cm Calculate areas: $$A_1 = 3 \times 4 = 12\text{ cm}^2$$ $$A_2 = 9 \times 4 = 36\text{ cm}^2$$ Total area: $$A = 12 + 36 = 48\text{ cm}^2$$ (7) Large L-shaped figure: split into two rectangles: - Rectangle 1: 90 m by 25 m - Rectangle 2: (80 - 25) m by 30 m = 55 m by 30 m Calculate areas: $$A_1 = 90 \times 25 = 2250\text{ m}^2$$ $$A_2 = 55 \times 30 = 1650\text{ m}^2$$ Total area: $$A = 2250 + 1650 = 3900\text{ m}^2$$ Final answers: (1) 49 m^2 (2) 225 cm^2 (3) 78 cm^2 (4) 162 m^2 (5) 72 cm^2 (6) 48 cm^2 (7) 3900 m^2 This completes the area calculations using the formula $P = \text{Area}$ for each figure.