# Area of Goalbox vs. Area of Penalty Box (rationals)

• mike_302
In summary, the size of the penalty box on a soccer field is approximately 2.44 times greater than the size of the goal box. This can be represented as a ratio of (22x^2)/9 : (10x^2)/27 or as a fraction of (22x^2)/9 over (10x^2)/27, which simplifies to 27/5.
mike_302

## Homework Statement

Area of goal box (soccer field) is described with (10x^2) / 27 and area of penalty box is described with (22x^2) / 9 . Determine how many times greater in size the penalty box is compared to the goal box.

## The Attempt at a Solution

I created the areas of the boxes based from dimensions, and simplified to what I have given (assume they are correct). Just don't get how to figure out that size difference (which is terrible since I just completed this question on the Fermat math contest for Waterloo earlier today, no problem, but I get thrown off in even easier math?)

read the question again. you don't even have to know the areas... it is simply asking for a ratio between the two

well ya... Simple ratio is (10x^2)/27 : (22x^2)/9 ... sooo.. would I then put that into fraction form (not sure which on top vs bottom for this situation), then simplify as far as possible...?

"Determine how many times greater in size the penalty box is compared to the goal box."
You want "penalty box" over "goal box".

(22x^2) / 9 over (10x^2) / 27 which is the same as (22x^2)/9 times 27/(10x^2).

## 1. What is the difference between the area of the goalbox and the penalty box?

The goalbox and penalty box are both rectangular areas on a soccer field, but they serve different purposes. The goalbox is the smaller of the two and is located within the penalty box. It is used for goalkeepers to safely handle the ball and for goal kicks. The penalty box, also known as the 18-yard box, is where certain fouls committed by the defending team result in a penalty kick for the attacking team.

## 2. How are the areas of the goalbox and penalty box determined?

The dimensions of the goalbox and penalty box are determined by the laws of the game set by the International Football Association Board. The goalbox is typically 6 yards by 20 yards, while the penalty box is 18 yards by 44 yards. However, these dimensions may vary slightly depending on the size of the field and the level of play.

## 3. Why is the goalbox smaller than the penalty box?

The goalbox is smaller than the penalty box because it is intended for the goalkeeper to have a smaller area to defend and control the ball. This allows for a fairer competition between the goalkeeper and the attacking team. Additionally, a smaller goalbox helps prevent the goalkeeper from handling the ball for an extended period of time, which would result in a violation.

## 4. Can players from the defending team enter the goalbox or penalty box?

Yes, players from the defending team are allowed to enter both the goalbox and penalty box. However, there are certain rules and restrictions in place. For example, defenders cannot enter the goalbox when the goalkeeper is holding the ball or interfere with the goalkeeper's ability to release the ball.

## 5. Are the areas of the goalbox and penalty box the same in all soccer leagues?

No, the dimensions of the goalbox and penalty box may vary slightly between leagues and organizations. For example, in youth soccer, the goalbox may be smaller to accommodate for the smaller size of the players. It is important for players to familiarize themselves with the specific dimensions of the goalbox and penalty box in their league or competition.

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