Question

The total fencing around a square field is 80 yards. The field has an area of how many square yards?

Answer 1

ANSWER

The field has an area of

`400 \: square \: yards`



Step-by-step explanation

The total fencing around a square field gives the total distance around the square field.


The total fencing around the field being

`80`
yards means, the perimeter is 80 yards.




Recall that the perimeter of a square is given by the formula,


`perimeter = 4l`


This implies that,


`80 = 4l`


We divide both sides by 4 to get,


`(80)/(4) = l`


This implies that

`l = 20 \: units`

We now obtain the area of the square by using the formula,


`A rea= {l}^(2)`

`A rea= {(20)}^(2) = 400 \: \: square \: \: yards`

Answer 2

The side length of the square is 1/4 of its perimeter, so is 20 yards. The area of the square is the square of its side length, so is (20 yd)² = 400 yd².