The perimeter of polygon ABCDE is 20.31 units.
Step-by-step explanation:
Step 1; First we plot points A, B, C, D and E on the graph. Coordinates are A (-3, 2), B (1, 2), C (3, -1), D(0, -3) and E (-4, -3). We need to find the distance between the 5 sides of the polygon i.e AB, BC, CD, DE, and AE.
Step 2; The sides AB and AE can be measured directly as they are horizontal lines. The x coordinate for A is -3 while for B it is 1, so distance is 1-(-3) = 4 units. The x coordinate for E is -4 while for D it is 0, so the distance is 0- (-4) = 4 units.
Step 3; To find the distances of BC, CD, and AE we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between B (1, 2) and C (3, -1) where B is (x1, y1) and C is (x2, y2).
Distance = √(3 - 1)² + (-1 -2)² = √4 + 9 = √13 = 3.605 units.
Distance between C (3, -1) and D (0, -3) where C is (x1, y1) and D is (x2, y2).
Distance = √(0 -3)² + (-3 -(-1))² = √9 + 4 = √13 = 3.605 units.
Distance between A (-3, 2) and E (-4, -3) where D is (x1, y1) and E is (x2, y2).
Distance = √(-4 -(-3))² + (-3 -2)² = √1 + 25 = √26 = 5.099 units.
Step 2; The parameter of this polygon is given by summing the lengths of the 4 sides.
Parameter = AB + BC + CD + DE + AE = 4 + 3.605 + 3.605 + 4 + 5.099 = 20.309 units. This is rounded off to 20.31 units.
