Finding Perimeter of a Polygon

The Perimeter

• The perimeter is the distance around an object, shape, or figure.
• To find the perimeter of a polygon, add up the length of all its sides.

Triangle and Rectangle Perimeters

• To find the perimeter of a rectangle, add up the length of all its sides (e.g., 80 + 80 + 80 + 80) or multiply the number of sides by the length of one side (e.g., 4 * 80).
• Melody's block has a perimeter of 320 ft, so she will walk 960 ft every day (3 times around the block).
• Daniel's rectangular bulletin board has a perimeter of 26 ft, but he only has 25 ft of decorative border, so it's not enough to line the entire board.
• Christy's triangular collage has a perimeter of 48 in, so she needs 48 in of ribbon to frame it, which will cost 3(4ft∗3 (4 ft * 3(4ft∗0.75 per ft).

Solving with Perimeter

• To find the measure of a side, use the perimeter and the formula for the perimeter of a rectangle or triangle.
• For rectangle DOTS, the perimeter is 56, and the length is 2x - 3, while the width is x + 1.
• To find the length of rectangle DOTS, solve for x by setting up the equation 2(2x - 3) + 2(x + 1) = 56, and then plug x = 10 into the equation for the length to get 2(10) - 3 = 17.
• For triangle PUD, the perimeter is 162 cm, and the sides are PD = 2x - 4, PU = x - 8, and UD = 3x - 15.
• To find the length of each side of triangle PUD, solve for x by setting up the equation 2x - 4 + x - 8 + 3x - 15 = 162, and then plug x = 31.5 into each equation to get PD = 59 cm, PU = 23.5 cm, and UD = 79.5 cm.