Find the perimeter of the polygon with the vertices Q(-3,2), R(1,2), S(1,-2) and T(-3,-2)
To find the perimeter of the polygon, we need to calculate the distance between each pair of adjacent vertices and then sum them all up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the vertices.
Distance between Q and R:
dQR = sqrt((1 - (-3))^2 + (2 - 2)^2)
= sqrt((4)^2 + (0)^2)
= sqrt(16)
= 4
Distance between R and S:
dRS = sqrt((1 - 1)^2 + (-2 - 2)^2)
= sqrt((0)^2 + (-4)^2)
= sqrt(16)
= 4
Distance between S and T:
dST = sqrt((-3 - 1)^2 + (-2 - 2)^2)
= sqrt((-4)^2 + (-4)^2)
= sqrt(16 + 16)
= sqrt(32)
= 4sqrt(2)
Distance between T and Q:
dTQ = sqrt((-3 - (-3))^2 + (-2 - 2)^2)
= sqrt((0)^2 + (-4)^2)
= sqrt(16)
= 4
Now, sum up the distances to find the perimeter:
Perimeter = dQR + dRS + dST + dTQ
= 4 + 4 + 4sqrt(2) + 4
= 8 + 4sqrt(2)
Therefore, the perimeter of the given polygon is 8 + 4sqrt(2).
To find the perimeter of a polygon, you need to calculate the sum of the lengths of all its sides. In this case, we have a quadrilateral with vertices Q(-3,2), R(1,2), S(1,-2), and T(-3,-2).
First, we need to find the lengths of each side. The distance formula can be used to calculate the distance between two points in a coordinate plane. The distance formula is:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Let's calculate the distances between the vertices:
1. Distance between Q and R:
distance = √[(1 - (-3))² + (2 - 2)²]
= √[4² + 0²]
= √(16 + 0)
= √16
= 4
2. Distance between R and S:
distance = √[(1 - 1)² + (-2 - 2)²]
= √[0² + (-4)²]
= √(0 + 16)
= √16
= 4
3. Distance between S and T:
distance = √[(-3 - 1)² + (-2 - (-2))²]
= √[(-4)² + 0²]
= √(16 + 0)
= √16
= 4
4. Distance between T and Q:
distance = √[(-3 - (-3))² + (-2 - 2)²]
= √[0² + (-4)²]
= √(0 + 16)
= √16
= 4
Now, we can find the perimeter by summing up the lengths of all sides:
perimeter = distance(QR) + distance(RS) + distance(ST) + distance(TQ)
= 4 + 4 + 4 + 4
= 16
Therefore, the perimeter of the given polygon is 16 units.
d1 = sqrt [ (2-2)^2 + (1+3)^2 ]
d2 = sqrt [ (-2-2)^2 + (1-1)^2 ]
d3 = sqrt [ (-2+2)*2 +(-3-1)^2 ]
d4 = sqrt[ (2+2)^2 + (-3+3)^2 ]
add the four lengths