ACT Math : How to find the perimeter of a polygon

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Polygon

Polygon

All segments of the polygon meet at right angles (90 degrees). The length of segment \overline{AB} is 10. The length of segment \overline{BC} is 8. The length of segment \overline{DE} is 3. The length of segment \overline{GH} is 2.

Find the perimeter of the polygon.

Possible Answers:

\dpi{100} \small 44

\dpi{100} \small 42

\dpi{100} \small 48

\dpi{100} \small 46

\dpi{100} \small 40

Correct answer:

\dpi{100} \small 46

Explanation:

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long \dpi{100} \small (10+2=12). The left and right sides would be 11 units long \dpi{100} \small (8+3=11). Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

Example Question #2 : How To Find The Perimeter Of A Polygon

In the figure below, each pair of intersecting line segments forms a right angle, and all the lengths are given in feet. What is the perimeter, in feet, of the figure?

 

Quad

Possible Answers:

Correct answer:

Explanation:

Fill in the missing sides by thinking about the entire figure as a big rectangle. In the figure below, the large rectangle is outlined in blue and the missing numbers are supplied in red.

 

Quad

Example Question #3 : How To Find The Perimeter Of A Polygon

What is the perimeter of a regular,  polygon with a side length of ?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of an -sided polygon with a side length of , simply multiply the side length by the number of sides:

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