Subjects geometry

Attic Surface Area 0210A4

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1. **State the problem:** Calculate the surface area of the attic given by the expression $$45 (40 + 25 + 25) + \frac{1}{2} (40 \times 15)$$. 2. **Understand the formula:** The expression consists of two parts: - The first part, $$45 (40 + 25 + 25)$$, likely represents the area of rectangular sections. - The second part, $$\frac{1}{2} (40 \times 15)$$, represents the area of a right triangle with base 40 ft and height 15 ft. 3. **Calculate the sum inside the parentheses:** $$40 + 25 + 25 = 90$$ 4. **Multiply by 45:** $$45 \times 90 = 4050$$ 5. **Calculate the area of the triangle:** $$\frac{1}{2} \times 40 \times 15 = \frac{1}{2} \times 600 = 300$$ 6. **Add both parts to find total surface area:** $$4050 + 300 = 4350$$ 7. **Final answer:** The surface area of the attic is **4350 square feet**.