1. **Stating the problem:** We have a wooden hanging bookshelf shaped like a house. The top part is a triangle with height 12 cm and side lengths 35 cm. Below it are two rectangular sections labeled "Atas" and "Bawah." The total width of the bookshelf is 42 cm. 2. **Understanding the shape:** The top triangle has a height of 12 cm and two equal sides of 35 cm. The base of this triangle is the width of the bookshelf, 42 cm. 3. **Calculate the area of the triangular top:** We can find the area of the triangle using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Substitute the values: $$\text{Area} = \frac{1}{2} \times 42 \times 12 = 21 \times 12 = 252 \text{ cm}^2$$ 4. **Check the side lengths consistency:** Using the Pythagorean theorem, check if the triangle with sides 35 cm and base 42 cm and height 12 cm is possible. Half the base is $\frac{42}{2} = 21$ cm. Calculate the length of the side using height and half base: $$\sqrt{12^2 + 21^2} = \sqrt{144 + 441} = \sqrt{585} \approx 24.19 \text{ cm}$$ Since the given side length is 35 cm, which is longer than 24.19 cm, the triangle is possible but not a right triangle. The height is given, so the side length is consistent with a triangle with height 12 cm. 5. **Summary:** The top triangle area is 252 cm², the width of the bookshelf is 42 cm, and the height of the triangle is 12 cm. 6. **Regarding the books thickness:** - 5 books each 4 cm thick: total thickness $5 \times 4 = 20$ cm. - 6 books each 3 cm thick: total thickness $6 \times 3 = 18$ cm. - 7 books each 2 cm thick: total thickness $7 \times 2 = 14$ cm. The user marked 6 books with 3 cm thickness as "Cukup" (enough), meaning the shelf can hold 18 cm thickness of books. **Final answer:** The triangular top area is $252$ cm², the bookshelf width is $42$ cm, and the height of the triangle is $12$ cm. The shelf can hold books with total thickness up to at least 18 cm based on the user's selection.