Add segments to the diagram and look for rectangles.
C
Practice makes perfect
The perimeter of a polygon is the sum of the length of the sides. On the given figure, the length of two sides is not given. Let's use x and y to denote the length of these sides. We will first find these measures.
On the figure, two angles of the polygon are indicated to be right angles. We will assume that all the other angles are also right angles.
Finding the Missing Horizontal Side Length
Extend the horizontal side of the polygon to create two rectangles. We know that opposite sides of a rectangle are congruent, so the lower horizontal side of the blue rectangle is also 4 centimeters long.
This means that the upper horizontal side of the green rectangle is 4+4=8 centimeters long. Since the opposite sides of the green rectangle are also congruent, this gives us the value of x.
x=8
Finding the Missing Vertical Side Length
This time let's cut the polygon into two rectangles with a vertical line. Again, the opposite sides of a rectangle are congruent, so both vertical sides of the blue rectangle are 3 centimeters long.
Comparing the vertical sides of the green rectangle gives us an equation to solve for y.
The perimeter of the figure is 28cm, so the correct answer is C.
Alternative Solution
Alternative way of thinking
Instead of cutting the figure to rectangles, we can add a rectangle to the figure to form a larger rectangle. Since the opposite sides of the blue rectangle are congruent, we can see that the perimeter of the original figure and the perimeter of the larger rectangle are the same.
The sides of the larger rectangle are l=4+4=8cm and w=6cm. We can use the formula P=2l+2w to find the perimeter.
