Question

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

Answer 1

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.

Answer 2

ANSWER

The field has an area of
$400 \: square \: yards$



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,

$\frac{80}{4} = l$


This implies that
$l = 20 \: units$

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

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