POLYGONS ON THE COORDINATE PLANE

Use the coordinates to find the length of each side of the rectangle. Then find the perimeter.

Problem 1 :

R(1, 1), S(1,7), T(5,7), U(5,1)

Solution :

By plotting the given points on the coordinate plane, we get

From the graph,

Length of the each side of the rectangle are 

AB = 4 units, BC = 6 units, CD = 4 units, and AD = 6 units

Perimeter of the rectangle = sum of all its four sides

= AB + BC + CD + AD

= 4 + 6 + 4 + 6

= 20 units

Problem 2 :

E(3, 6), F(7, 6), G(7, 2), H(3, 2)

Solution :

By plotting the given points on the coordinate plane, we get

From the graph,

Length of the each side of the rectangle are 

AB = 4 units, BC = 4 units, CD = 4 units, and AD = 4 units

Perimeter of the rectangle = sum of all its four sides

= AB + BC + CD + AD

= 4 + 4 + 4 + 4

= 16 units

Problem 3 :

E(1, 7), F(3, 7), G(3, 4), H(1, 4)

Solution :

By plotting the given points on the coordinate plane, we get

From the graph,

Length of the each side of the rectangle are 

AB = 2 units, BC = 3 units, CD = 2 units, and AD = 3 units

Perimeter of the rectangle = sum of all its four sides

= AB + BC + CD + AD

= 2 + 3 + 2 + 3

= 10 units

Problem 4 :

W(2, 7), X(2, 0), Y(6, 0), Z(6, 7)

Solution :

By plotting the given points on the coordinate plane, we get

From the graph,

Length of the each side of the rectangle are 

AB = 4 units, BC = 7 units, CD = 4 units, and AD = 7 units

Perimeter of the rectangle = sum of all its four sides

= AB + BC + CD + AD

= 4 + 7 + 4 + 7

= 22 units

Problem 5 :

Plans for a patio are shown in the coordinate plane at the left. The coordinates are measured in feet. Find the perimeter and the area of the patio.

Solution :

Perimeter of the rectangle = Length of (QR + RS + ST + TQ)

Length of QR = 8 units

Length of RS = 6 units

Length of ST = 8 units

Length of QT = 6 units

= 8 + 6 + 8 + 6

= 16 + 12

= 28 units

So, the perimeter of the rectangle is 28 units.

Area of rectangle = length x width

= 8 x 6

= 48 square units.

Problem 6 :

Find the perimeter and the area of the polygon with the given vertices.

C(1, 1), D(1, 4), E(4, 4), F (4, 1)

Solution :

• Distance between DF = 3 units
• Distance between EF = 3 units
• Distance between DF = 3 units
• Distance between DC = 3 units

Since all sides are equal, then it must be a square.

Perimeter of square CDEF = 4(3)

= 12 units

Area of square = 3 x 3

= 9 square units

Problem 7 :

Find the perimeter and the area of the polygon with the given vertices.

J (1, 2), K (7, 2), L(7, 8), M (1, 8)

Solution :

• Distance between JK = 6 units
• Distance between KL = 6 units
• Distance between LM = 6 units
• Distance between MJ = 6 units

Since all sides are equal, then it must be a square.

Perimeter of square JKLM = 4(6)

= 24 units

Area of square = 6 x 6

= 36 square units

Problem 8 :

Find the perimeter and the area of the polygon with the given vertices.

N(0, 2), P (5, 2), Q (5, 5), R (0, 5)

Solution :

• Distance between NP = 5 units
• Distance between PQ = 5 units
• Distance between QR = 5 units
• Distance between RN = 5 units

Since all sides are equal, then it must be a square.

Perimeter of square NPQR = 4(5)

= 20 units

Area of square = 5 x 5

= 25 square units

Problem 9 :

Find the perimeter and the area of the polygon with the given vertices.

use the diagram.

a)  Find the area of triangle ABD

b) Find the area of triangle BCD

c) Area of quadrilateral ABCD

Solution :

a)  Finding the area of triangle ABD :

Base = 6 units

height = 5 units

Area of triangle ABD = (1/2) x base x height

= (1/2) x 6 x 5

= 3 x 5

= 15 square units

b) Finding the area of triangle BCD :

Base = 6 units

height = 4 units

Area of triangle BCD = (1/2) x 6 x 4

= 12 square units

c) Finding the area of quadrilateral ABCD = 15 + 12

= 27 square units