Question

The blueprint for a circular gazebo has a scale of 2 inches=5 feet. The blueprint shows that the gazebo has a diameter of 5.1 inches. What is the actual diameter of the​ gazebo? What is its​ area? Use 3.14 for π.

Answer 1

• 12.75 ft
• 127.61 ft²

Explanation:

You want to know the actual diameter and the area of a circular gazebo shown with a diameter of 5.1 inches on a drawing with a scale of 2 inches to 5 ft.

Diameter

The actual diameter is proportional to the drawing diameter according to the drawing scale:

d/(5.1 in) = (5 ft)/(2 in)

d = (5.1 in)(5 f)/(2 in) = 12.75 ft

The diameter of the gazebo is 12.75 ft.

Area

The area can be computed using ...

A = (π/4)d²

A = (3.14/4)(12.75 ft)² = 127.6115625 ft² ≈ 127.61 ft²

The area of the gazebo is about 127.61 square feet.

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Additional comment

You could round this to 127.6 or 128 square feet as may be required by your grader.

Based on the drawing dimension being given to 2 significant figures, the area could even be rounded to 2 significant figures: 130 ft².

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