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2 years ago

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Mathematics

1 answer:

asambeis [7]2 years ago

3 0

Answer:

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.

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