Question

Ramon was plotting the coordinates of a polygon. He has plotted the coordinates of the polygon shown below. What is the area of Ramon's

polygon?

1. Point A (2.5)

2. Point B (8,5)

3. Point C (8,9)

4. Point D (5,7)

5. Point E (2.9)

V

E

C

9

8

D

7

6

ke

5

A

B

4

3

2

1

5

6

7

8

9.

Answer 1

Area of polygon = 18

Explanation:

the given points are :

Point A (2.5)

Point B (8,5)

Point C (8,9)

Point D (5,7)

Point E (2,9)

Firstly , create the array

A 2 5

B 8 5

C 8 9

D 5 7

E 2 9

A 2 5

Now,

Multiply the x coordinates of each vertex by the y coordinate of the next vertex . and then add the result.

⇒ 10 + 72 + 56 + 45 + 10 = 193 .......(1)

Now,

Multiply the y coordinate of each vertex by the x coordinate of next vertex. then add the result

⇒ 40 + 40 + 45 + 14 + 18 = 157 ........(2)

Now, Subtract equation (2) from equation (1), we get

193 - 157 = 36

Now, Divide by 2 to get the area of polygon

∴ we get

Area of polygon = 18