1. **State the problem:** We need to find the weight of a wooden headboard shaped like a house with given dimensions. 2. **Identify the shape and dimensions:** The headboard consists of a rectangle and a triangular roof on top. - Width of the base (rectangle): $1.8$ m - Height of the rectangle: $0.7$ m (right side height) - Heights of the left and right sides differ, so the roof is asymmetric. - The roof has two horizontal segments of $0.5$ m each and a peak in the middle. - Left vertical height to the roof peak: $1.1$ m 3. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = \text{width} \times \text{height} = 1.8 \times 0.7 = 1.26 \text{ m}^2$$ 4. **Calculate the area of the roof (two triangles):** The roof can be split into two right triangles on each side of the peak. - Left triangle height: $1.1 - 0.7 = 0.4$ m - Right triangle height: $0.7 - 0.7 = 0$ m (since right height is base height, no right triangle) - Base of each triangle: $0.5$ m Area of left triangle: $$\frac{1}{2} \times 0.5 \times 0.4 = 0.1 \text{ m}^2$$ Area of right triangle is zero because height difference is zero. 5. **Calculate total area:** $$\text{Area}_{total} = 1.26 + 0.1 = 1.36 \text{ m}^2$$ 6. **Calculate weight:** Given $1 \text{ m}^2$ of wood weighs $23$ kg, $$\text{Weight} = 1.36 \times 23 = 31.28 \text{ kg}$$ 7. **Final answer:** The headboard weighs approximately **31.28** kg.