Question

expression for surface area of attic:
$45 (40 + 25 + 25) + \frac{1}{2}(40 \times 15)$

click the arrows to choose an answer from each menu to explain your reasoning.
the net linda drew is choose... . the first term of linda’s expression,
$45 (40 + 25 + 25)$, choose... . the second term of linda’s expression,
$\frac{1}{2}(40 \times 15)$, is choose... . the surface area of linda’s attic is
choose... square feet.

Explanation:

Step1: Analyze the first term

The first term is \( 45(40 + 25 + 25) \). First, calculate the sum inside the parentheses: \( 40+25 + 25=90 \). Then multiply by 45: \( 45\times90 = 4050 \). This term likely represents the area of the rectangular parts of the attic's net.

Step2: Analyze the second term

The second term is \( \frac{1}{2}(40\times15) \). Calculate \( 40\times15 = 600 \), then multiply by \( \frac{1}{2} \): \( \frac{1}{2}\times600 = 300 \). This term represents the area of the triangular part (since the formula for the area of a triangle is \( \frac{1}{2}\times base\times height \), here base is 40 and height is 15).

Step3: Calculate the total surface area

Add the two terms together: \( 4050+300 = 4350 \).

Answer:

The surface area of Linda’s attic is \(\boldsymbol{4350}\) square feet. (For the other "Choose..." parts, assuming typical attic net structure: The net Linda drew is a combination of rectangles and a triangle. The first term \( 45(40 + 25 + 25) \) is the area of the rectangular faces. The second term \( \frac{1}{2}(40\times15) \) is the area of the triangular face. But since the question's dropdowns are not visible, the calculated surface area is 4350.)