Subjects geometry

Wainscoting Area E1F39E

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1. **State the problem:** Mrs. Hernandez wants to add wainscoting halfway up the walls of her craft room, which is a rectangular prism with dimensions 12 ft (length), 9 ft (width), and 8 ft (height). There are two doors, each 3 ft wide and 4 ft high, and we need to find the total square feet of wainscoting required. 2. **Formula and explanation:** - The total surface area of the walls is given by the perimeter times the height. - Wainscoting covers only halfway up the walls, so height for wainscoting is $\frac{8}{2} = 4$ ft. - The perimeter $P$ of the room is $2(L + W) = 2(12 + 9) = 42$ ft. - Total wall area for wainscoting is $P \times 4 = 42 \times 4 = 168$ ft$^2$. - Subtract the area of the doors from this total. 3. **Calculate door area:** - Each door area = height $\times$ width = $4 \times 3 = 12$ ft$^2$. - Two doors area = $12 \times 2 = 24$ ft$^2$. 4. **Calculate wainscoting area:** $$\text{Wainscoting area} = 168 - 24 = 144 \text{ ft}^2$$ 5. **Final answer:** Mrs. Hernandez will need **144 square feet** of wainscoting to cover halfway up the walls, excluding the doors.