English Perimeter and Area of Rhombi, Trapezoids, and Kites
Instruction Active
Finding the Perimeter of a Trapezoid in the Coordinate
Plane
What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest
hundredth, if necessary.
units
O Tuto

38.25 units.

Step-by-step explanation:

The trapezoid is given with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)

When given vertices ( x1, y1), (x2, y2)

We use the formula:

√(x2 - x1)² + (y2 - y1)² to find the length of the sides of the Trapezoid

Side QR: Q(8, 8), R(14, 16)

= √(x2 - x1)² + (y2 - y1)²

= √(14 - 8)² + (16 - 8)²

= √6² + 8²

= √36 + 64

= √100

= 10 units

Side RS: R(14, 16), S(20, 16)

= √(x2 - x1)² + (y2 - y1)²

= √(20 - 14)² + (16 - 16)²

= √6² + 0²

= √36

= 6 units

Side ST : S(20, 16), T(22, 8)

= √(x2 - x1)² + (y2 - y1)²

= √(22 - 20)² + ( 8 - 16)²

= √2² + (-8)²

= √4 + 64

= √68

= 8.2462112512

≈ nearest hundredth = 8.25 units

Side QT, Q(8, 8), T(22, 8)

= √(x2 - x1)² + (y2 - y1)²

= √(22 - 8)² + (8 - 8)²

= √14² + 0²

= √196

= 14 units

The Perimeter of a Trapezoid is the sum of all it's sides.

P = QR + RS + ST + QT

P = (10 + 6 + 14 + 8.25) units

P = 38.25 units

Therefore, the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8) is 38.25units.