The diagram shows the dimensions of a house. The door and the peak of the roof are centered in the view. A contractor uses the diagram to estimate the square footage of the roof and the cost to shingle the roof.

Calculate the missing dimension in the diagram. Round your answer to the nearest whole number. Show your work.

1 answer

To help you calculate the missing dimension in the diagram related to the dimensions of the house and the roofing, I would need more specific information or values presented in the diagram.

Since I don’t have the diagram to refer to, I can provide you with a general approach on how to find a missing dimension based on common scenarios involving rooftops.

Example Calculation Process:

  1. Identify Given Information:

    • For example, if the width of the house is given and the pitch of the roof (which is the angle of the slope) is known, this could help in figuring out the height at the peak.
  2. Use Geometry:

    • If you know the width (W) of the house and need to find the height (H) of the peak when given the pitch (rise/run), you could use a right triangle relationship.

    • For example, if the pitch of the roof is 12/4 (which means for every 12 units of run, the height increases by 4 units), you can form a right triangle with: \[ \text{pitch ratio} = \frac{\text{rise}}{\text{run}}. \]

  3. Calculate Using Triangle Properties:

    • If the total width is W, the run (half of the width) will be \( \frac{W}{2} \).
    • By using the slope ratio: \[ H = \text{pitch ratio} \times \frac{W}{2}, \]
    • Substitute the values you have.
  4. Finalizing your Answer:

    • Once you compute the height (or missing dimension), round it to the nearest whole number as needed.

If you can provide the relevant dimensions or any specifications from the diagram (e.g., width of the house, pitch of the roof), I can give you a more precise calculation tailored to your problem!