Question

An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the front of the garage?

The graph shows a five-edged polygon. The five edges are on (minus 5.5, 0), (minus 5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).

Answer 1

37.26 units

Explanation:

You want to know the perimeter of the pentagon defined by the points (-5.5, 0), (-5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).

Graph

The attached graph shows the points and the distances between them. The perimeter is the sum of those distances.

7 +6.13 +6.13 +7 + 11 = 37.26

The perimeter of the polygon is about 37.26 units.

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Additional comment

The length of the slant edges can be found using the distance formula.

d = √((x2 -x1)² +(y2 -y1)²) = √((0 -5.5)² +(9.7 -7)²) = √(30.25 +7.29)

= √37.54 ≈ 6.12699

The lengths of the horizontal and vertical edges can be found by differencing the x- and y-coordinates of the points, respectively. (The distance formula can be used, as well.)