Question

The verticles of a polygon p(0,4), q(5,4), r(5.-3) and s(0,-3). What are the perimeters of the polygon

Answer 1

Following are the responses to the given question:

Perimeter of polygon:

`PQ = 5\\\\RS = 5\\\\PR = QS=√(74) = 8.60\\\\QR = 7`

Explanation:

In this question we calculate the perimeter of a polygon which can be defined as follows:

Using formula:

`d = √((x _2 - x_1)^2 + (y_2 - y_1)^2)`

When vertices are:

`P ( 0 , 4) \\\\Q(5 , 4)`

`x_1 = 0\\\\y_1 = 4\\\\x_2 = 5\\\\y_2 = 4\\\\PQ = √(( 5 - 0)^2 + ( 4 - 4)^2)\\\\= √(5^2 + 0^2)\\\\= √(25)\\\\= 5`

`R( 5 , -3) and S ( 0 , -3)x_1 = 5y_1 = -3x_2 = 0\\y_2 = -3\\RS = √( ( 0 - 5)^2 + ( -3 - (-3))^2)\\= √(( -5)^2 + ( -3 + 3)^2)\\= √( 25 + 0)\\= √(25)\\= 5\\P( 0 , 4)\ and\ R (5 , -3)\\x_1 = 0\\y_1 = 4\\x_2 = 5\\y_2 = -3\\PR = √(( 5 - 0)^2 + ( -3 - 4)^2)\\= √(5^2 + (-7)^2)\\= √( 25 + 49)\\= √(74)\\= 8.60\\`

`Q ( 5 , 4) \ and \ S(0 ,-3)\\x_1 = 5\\y_1 = 4\\x_2 = 0\\y_2 = -3\\QS =√( ( 0 - 5)^2 + ( -3 - 4)^2)\\= √(-5^2 + -7^2)\\= √(25 + 49)\\= √(74)\\= 8.60`

`Q( 5,4\ and\ R(5 , -3)\\x_1 = 5\\y_1 = 4\\x_2 = 5\\y_2 = -3\\QR = √((5 - 5)^2 + ( -3 - 4)^2)\\= √(0^2 + (-7)^2)\\= √(0 + 49)\\= √(49)\\= 7\\`