Find the perimeter of a quadrilateral with vertices at C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2). Round your answer to the nearest hundredth when necessary.
10 units
10.77 units
11.52 units
12.35 units
Answers
Answer:
Perimeter of quadrilateral = 12.35 units
Explanation:
To find - Find the perimeter of a quadrilateral with vertices at C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2).
Proof -
The figure becomes :
We have the points -
C (−2, 4),
D (−3, 1),
E (1, 0),
F (−1, 2)
Now,
We know that -
The perimeter = Distance of (CD + DE + EF + FC)
Now,
Distance of CD = √(-3 + 2)² + (1 - 4)²
= √(-1)² + (-3)²
= √1 + 9
= √10 = 3.16
⇒Distance of CD = 3.16
Now,
Distance of DE = √(1 + 3)² + (0 - 1)²
= √(4)² + (-1)²
= √16 + 1
= √17 = 4.12
⇒Distance of DE = 4.12
Now,
Distance of EF = √(-1 - 1)² + (2 - 0)²
= √(-2)² + (2)²
= √4 + 4
= √8 = 2.83
⇒Distance of EF = 2.83
Now,
Distance of FC = √(-2 + 1)² + (4 - 2)²
= √(-1)² + (2)²
= √1 + 4
= √5 = 2.24
⇒Distance of FC = 2.24
So,
Perimeter of quadrilateral = 3.16 + 4.12 + 2.83 + 2.24
= 12.35 units
⇒Perimeter of quadrilateral = 12.35 units
Based on the information given, the perimeter of the quadrilateral will be 12.35 units.
Calculating the perimeter.From the information given the distance of CD will be:
= ✓1 + ✓9
= 3.16
The distance of DE will be:
= ✓16 + ✓1
= 4.12
The distance of EF will be;
= ✓4 + ✓4
= 2.83
The distance of FC will be:
= ✓1 + ✓4
= 2.24
Therefore, the perimeter will be:
= 3.16 + 4.12 + 2.83 + 2.24
= 12.35 units
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