Question

Find the perimeter of the polygon with the given vertices: P(1, 2), Q(1, 6), R(8, 6), S(8, 2).

a) 22 units
b) 26 units
c) 30 units
d) 32 units

Answer 1

The perimeter of the polygon with vertices P(1, 2), Q(1, 6), R(8, 6), and S(8, 2) is found by summing the lengths of its sides, which results in 22 units. The correct answer option is (a) 22 units.

Step-by-step explanation:

The question asks for the perimeter of a polygon with given vertices P(1, 2), Q(1, 6), R(8, 6), and S(8, 2). To find the perimeter, we calculate the distances between consecutive vertices, which are also the sides of the polygon.

• PQ is vertical and has the same x-value, so its length is |6 - 2| = 4 units.
• QR is horizontal and has the same y-value, so its length is |8 - 1| = 7 units.
• RS is vertical and has the same x-value, so its length is |6 - 2| = 4 units.
• SP is horizontal and has the same y-value, so its length is |8 - 1| = 7 units.

The perimeter (P) is therefore P = PQ + QR + RS + SP = 4 + 7 + 4 + 7 = 22 units.

The correct answer is (a) 22 units.