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

2 answers:

7 0

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.

Karolina [17]3 years ago

4 0

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,

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

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A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as s

Pepsi [2]

Answer:

$3\sqrt{3} + 72$

Step-by-step explanation:

I attached an image to aid the understanding of the question.

Looking at the image, we see that the 8 shaded parts are congruent, as affirmed in the question as well. And we are told that T = 3, this implies that the area of the square with T as it's side is 9ft². Since all the 8 squares are congruenrt, it means each square has its area to be 9. Therefore, the total area of the 8 shaded squares will be:

$9 \times 8 = 72ft^{2}$

It remains the area of the shaded square with side S.

From the question, we have the following ratio:

$\frac{9}{S} = \frac{S}{T}[\tex]But[tex]\frac{9}{S} = \frac{S}{3}[\tex]Multiplying through by 3S we have27 = S² and this gives:[tex]S = \sqrt{27} = 3\sqrt{3}$