Question:
Find the perimeter of the following shape, rounded to the nearest tenth: Shape ABCD is shown. Point A is at negative 3, 5. Point B is at 1, 7. Point C is at 3, 3. Point D is at negative 1, 1.
a) 12
b) 13.9
c) 17.9
d) 20
c) 17.9
Step-by-step explanation:
In the question, we are given the following points
Point A is at negative 3, 5. = (-3, 5)
Point B is at 1, 7 = (1, 7)
Point C is at 3, 3 = (3, 3)
Point D is at negative 1, 1 = (-1, 1)
When we are given points (x₁, y₁) and ( x₂ , y₂) we would use the formula
√(x₂ - x₁)² + (y₂ - y₁)²
For point A and Point B = AB
= √(x₂ - x₁)²+ (y₂ - y₁)²
= √(1 - (-3) )² + (7 - 5)²
= √(4² + 2²)
= √(16 + 4)
= √20
For point B and Point C = BC
= √(x₂ - x₁)²+ (y₂ - y₁)²
= √(3 - 1 )² + (3 - 7)²
= √(2² + (-4)²)
= √4 + 16
= √20
For point D and Point C = DC
= √(x₂ - x₁)²+ (y₂ - y₁)²
= √(-1 - (-3) )² + (1 - 3)²
= √(4² + -2²)
= √(16 + 4)
= √20
For point A and Point D = AD
= √(x₂ - x₁)²+ (y₂ - y₁)²
= √(-1 - (-3) )² + (1 - 5)²
= √(-2² + -4²)
= √(4 + 16)
= √20
From the solved calculations above, we can see that
AB = BC = DC = AD
This proves to us, that the above shape with points A, B, C and D is a square.
This is because the sides of a square are equal to one another
The formula for the perimeter of a square = 4 × Length of one side
Hence, the perimeter of this square in the above question =
4 × √20
17.88854382.
Approximately to the nearest tenth = 17.9
Therefore, the perimeter of the following shape ( Square) to the nearest tenth = 17.9
Step-by-step explanation: