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ACT Math : How to find the perimeter of a polygon

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Example Question #1 : Plane Geometry

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:

$\dpi{100} \small 42$

$\dpi{100} \small 40$

$\dpi{100} \small 48$

$\dpi{100} \small 44$

$\dpi{100} \small 46$

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.

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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

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Example Question #595 : Plane Geometry

What is the perimeter of a regular, $\textup{13-sided}$ polygon with a side length of $4\textup{cm}$ ?

Possible Answers:

$\textup{56cm}$

$\textup{44cm}$

$\textup{52cm}$

$\textup{4cm}$

$\textup{50cm}$

Correct answer:

$\textup{52cm}$

Explanation:

To find the perimeter of an -sided polygon with a side length of , simply multiply the side length by the number of sides:
$4\textup{cm}*13=52\textup{cm}$

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ACT Math : How to find the perimeter of a polygon

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Plane Geometry

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

Example Question #595 : Plane Geometry

All ACT Math Resources

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