How to find the perimeter of a polygon - ACT Math

Card 0 of 3

Question

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.

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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

Compare your answer with the correct one above

Tap the card to reveal the answer