DSQ: Calculating the area of a square - GMAT Quantitative
Card 1 of 48
Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Tap to reveal answer
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
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The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area 
.
The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area
Tap to reveal answer
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If 
is the sidelength of the square, then the length of its diagonal - which is also the diameter of the circle - is, by the Pythagorean Theorem, 
, and the radius 
. Therefore, if you calculate either the radius or the sidelength, you can calculate the other, allowing you to find the areas of the circle and the square.
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for 
in the equation 
.
Therefore, either one gives you enough information to solve the problem.
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for
Therefore, either one gives you enough information to solve the problem.
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A circle is inscribed inside Square 
. The circle intersects the square at points 
. Give the area of the square.
Statement 1: The circle has circumference 
.
Statement 2: 
is a 
arc.
A circle is inscribed inside Square
Statement 1: The circle has circumference
Statement 2:
Tap to reveal answer
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by 
to obtain this measure, and this can be squared to obtain the area of the square.
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that 
is one fourth of the circle and, subsequently, a 
arc.
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that
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A circle is inscribed inside Square 
. The circle intersects the square at points 
. Give the area of the square.
Statement 1: The circle has area 
.
Statement 2: Arc 
has length 
.
A circle is inscribed inside Square
Statement 1: The circle has area
Statement 2: Arc
Tap to reveal answer
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square, 
is one fourth of the circle, the length of 
can be multiplied by four to get the circumference of the circle. This can be divided by to obtain this diameter.
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square,
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
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Find the area square R
I) The diagonal of square R is 
.
II) The perimeter of square R is 
.
Find the area square R
I) The diagonal of square R is
II) The perimeter of square R is
Tap to reveal answer
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
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True or false: 
Statement 1: A square with sidelength 
has perimeter greater than 100.
Statement 2: A square with sidelength 
has area greater than 40.
True or false:
Statement 1: A square with sidelength
Statement 2: A square with sidelength
Tap to reveal answer
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is 
; the perimeter is greater than 100, so
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is 
, for example, the area is the square of this, which is 81; if the sidelength is 
, the area is 121. Both areas exceed 40, but only in the second case is 
.
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is
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Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Tap to reveal answer
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
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The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area .
The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area
Tap to reveal answer
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If is the sidelength of the square, then the length of its diagonal - which is also the diameter of the circle - is, by the Pythagorean Theorem, , and the radius . Therefore, if you calculate either the radius or the sidelength, you can calculate the other, allowing you to find the areas of the circle and the square.
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for in the equation .
Therefore, either one gives you enough information to solve the problem.
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for
Therefore, either one gives you enough information to solve the problem.
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A circle is inscribed inside Square . The circle intersects the square at points . Give the area of the square.
Statement 1: The circle has circumference .
Statement 2: is a arc.
A circle is inscribed inside Square
Statement 1: The circle has circumference
Statement 2:
Tap to reveal answer
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by to obtain this measure, and this can be squared to obtain the area of the square.
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that is one fourth of the circle and, subsequently, a arc.
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that
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A circle is inscribed inside Square . The circle intersects the square at points . Give the area of the square.
Statement 1: The circle has area .
Statement 2: Arc has length .
A circle is inscribed inside Square
Statement 1: The circle has area
Statement 2: Arc
Tap to reveal answer
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square, is one fourth of the circle, the length of can be multiplied by four to get the circumference of the circle. This can be divided by to obtain this diameter.
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square,
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
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Find the area square R
I) The diagonal of square R is .
II) The perimeter of square R is .
Find the area square R
I) The diagonal of square R is
II) The perimeter of square R is
Tap to reveal answer
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
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True or false:
Statement 1: A square with sidelength has perimeter greater than 100.
Statement 2: A square with sidelength has area greater than 40.
True or false:
Statement 1: A square with sidelength
Statement 2: A square with sidelength
Tap to reveal answer
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is ; the perimeter is greater than 100, so
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is , for example, the area is the square of this, which is 81; if the sidelength is , the area is 121. Both areas exceed 40, but only in the second case is .
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is
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Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Tap to reveal answer
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
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The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area .
The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area
Tap to reveal answer
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If is the sidelength of the square, then the length of its diagonal - which is also the diameter of the circle - is, by the Pythagorean Theorem, , and the radius . Therefore, if you calculate either the radius or the sidelength, you can calculate the other, allowing you to find the areas of the circle and the square.
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for in the equation .
Therefore, either one gives you enough information to solve the problem.
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for
Therefore, either one gives you enough information to solve the problem.
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A circle is inscribed inside Square . The circle intersects the square at points . Give the area of the square.
Statement 1: The circle has circumference .
Statement 2: is a arc.
A circle is inscribed inside Square
Statement 1: The circle has circumference
Statement 2:
Tap to reveal answer
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by to obtain this measure, and this can be squared to obtain the area of the square.
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that is one fourth of the circle and, subsequently, a arc.
The diameter of the inscribed circle is equal to the the sidelength of the square. From Statement 1, the circumference can be divided by
Statement 2 gives extraneous information, as, by regularity of the figure, it is already known that
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A circle is inscribed inside Square . The circle intersects the square at points . Give the area of the square.
Statement 1: The circle has area .
Statement 2: Arc has length .
A circle is inscribed inside Square
Statement 1: The circle has area
Statement 2: Arc
Tap to reveal answer
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square, is one fourth of the circle, the length of can be multiplied by four to get the circumference of the circle. This can be divided by to obtain this diameter.
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
From Statement 1, the radius of the circle can be calculated by working backwards from the area formula, and the diameter can be calculated by doubling this.
From Statement 2, since, by the regularity of the square,
This diameter is equal to the the sidelength of the square in which it is inscribed, so it can be squared to obtain the area of the square. This makes each statement alone sufficient to answer the question.
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Find the area square R
I) The diagonal of square R is .
II) The perimeter of square R is .
Find the area square R
I) The diagonal of square R is
II) The perimeter of square R is
Tap to reveal answer
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
You can use the diagonal of a square to find its side length via the ratio of a 45/45/90 triangle.
In this case our triangle will have side lengths of 15.
We can also divide our perimeter by 4 to get our side length, which is again 15.
Therefore, each statement alone is sufficient to solve the question.
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True or false:
Statement 1: A square with sidelength has perimeter greater than 100.
Statement 2: A square with sidelength has area greater than 40.
True or false:
Statement 1: A square with sidelength
Statement 2: A square with sidelength
Tap to reveal answer
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is ; the perimeter is greater than 100, so
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is , for example, the area is the square of this, which is 81; if the sidelength is , the area is 121. Both areas exceed 40, but only in the second case is .
Assume Statement 1 alone. The perimeter of a square is four times the length of a side, which here is
Therefore, the question can be answered in the affirmative from Statement 1 alone.
Statement 2 alone gives insufficient information, however. The area of a square is the square of the length of a side. If the sidelength is
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Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Data sufficiency question- do not actually solve the question
Find the area of a square.
1. The length of one side of the square is 4.
2. The length of the diagonal of the square is 12.
Tap to reveal answer
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
Because all 4 sides of a square are equal, knowing the length of one side is sufficient to answer the question. Using the Pythagorean Theorem, you can calculate the length of 1 side of a square by knowing the length of a diagonal and then calculate the area.
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The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area .
The above figure shows a square inscribed inside a circle. What is the area of the black region?
Statement 1: The square has perimeter 40.
Statement 2: The circle has area
Tap to reveal answer
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If is the sidelength of the square, then the length of its diagonal - which is also the diameter of the circle - is, by the Pythagorean Theorem, , and the radius . Therefore, if you calculate either the radius or the sidelength, you can calculate the other, allowing you to find the areas of the circle and the square.
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for in the equation .
Therefore, either one gives you enough information to solve the problem.
The area of the black region is one-fourth the difference of the areas of the circle and the square.
If
Statement 1 allows you to find the sidelength; just divide 40 by 4.
Statement 2 allows you to find the radius; just solve for
Therefore, either one gives you enough information to solve the problem.
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