Problem

4. Jack is building an all-glass gazebo. He will use glass on the roof and four walls. Below is a 3-D diagram with dimensions. $(4 \%)$ What amount of glass is required for the gazebo (ignoring frames around the glass)? Round your answer to the nearest square foot. Hint: Find the surface area of 4 triangles and 4 squares.

Solution

Step 1 :Find the surface area of the 4 triangles (roof) and 4 squares (walls).

Step 2 :Calculate the area of each triangle: \(A_{triangle} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 10 \times 6 = 30\)

Step 3 :Calculate the total area of the 4 triangles: \(A_{triangles} = 4 \times A_{triangle} = 4 \times 30 = 120\)

Step 4 :Calculate the area of each square (wall): \(A_{square} = side^2 = 10^2 = 100\)

Step 5 :Calculate the total area of the 4 squares: \(A_{squares} = 4 \times A_{square} = 4 \times 100 = 400\)

Step 6 :Add the total area of the triangles and squares: \(A_{total} = A_{triangles} + A_{squares} = 120 + 400 = 520\)

Step 7 :\(\boxed{520}\) square feet of glass is required for the gazebo.

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Source: https://solvelyapp.com/problems/22230/

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