How to find the perimeter of a square - GRE Quantitative Reasoning
Card 1 of 40
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
Tap to reveal answer
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
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What is the perimeter of a square that has an area of 81?
What is the perimeter of a square that has an area of 81?
Tap to reveal answer
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
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The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
Tap to reveal answer
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be 
.
Finally, the perimeter of a square is 
.
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be
Finally, the perimeter of a square is
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A square table has an area of 
square centimeters and a perimeter of 
centimeters.
If 
, what is the perimeter of the square?
A square table has an area of
If
Tap to reveal answer
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
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The diagonal of square 
is 
feet. Approximately how long in inches is the perimeter of square 
?
The diagonal of square
Tap to reveal answer
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that 
, where x is equal to the length of one side of the square.
This gives us 
.
Therefore, the perimeter of square 
is equal to 
.
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that
This gives us
Therefore, the perimeter of square
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The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
Tap to reveal answer
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
← Didn't Know|Knew It →
What is the perimeter of a square that has an area of 81?
What is the perimeter of a square that has an area of 81?
Tap to reveal answer
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
← Didn't Know|Knew It →
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
Tap to reveal answer
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be .
Finally, the perimeter of a square is .
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be
Finally, the perimeter of a square is
← Didn't Know|Knew It →
A square table has an area of square centimeters and a perimeter of centimeters.
If , what is the perimeter of the square?
A square table has an area of
If
Tap to reveal answer
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
← Didn't Know|Knew It →
The diagonal of square is feet. Approximately how long in inches is the perimeter of square ?
The diagonal of square
Tap to reveal answer
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that , where x is equal to the length of one side of the square.
This gives us .
Therefore, the perimeter of square is equal to .
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that
This gives us
Therefore, the perimeter of square
← Didn't Know|Knew It →
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
Tap to reveal answer
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
← Didn't Know|Knew It →
What is the perimeter of a square that has an area of 81?
What is the perimeter of a square that has an area of 81?
Tap to reveal answer
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
← Didn't Know|Knew It →
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
Tap to reveal answer
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be .
Finally, the perimeter of a square is .
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be
Finally, the perimeter of a square is
← Didn't Know|Knew It →
A square table has an area of square centimeters and a perimeter of centimeters.
If , what is the perimeter of the square?
A square table has an area of
If
Tap to reveal answer
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
← Didn't Know|Knew It →
The diagonal of square is feet. Approximately how long in inches is the perimeter of square ?
The diagonal of square
Tap to reveal answer
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that , where x is equal to the length of one side of the square.
This gives us .
Therefore, the perimeter of square is equal to .
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that
This gives us
Therefore, the perimeter of square
← Didn't Know|Knew It →
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
The diagram above represents a square ABCD with a semi-circle directly attached to its side. If the area of the figure is 16 + 2π, what is its outer perimeter?
Tap to reveal answer
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
We know that our area can be represented by the following equation:
Instead of solving the algebra, you should immediately note several things. 16 = 42 and 4 = 22. If the side of the square is 4, then s = 4 would work out as:
which is just what we need.
With s = 4, we know that 3 sides of our figure will have a perimeter of 12. The remaining semicircle will be one half of the circumference of a circle with diameter of 4; therefore it will be 0.5 * 4 * π or 2π.
Therefore, the outer perimeter of our figure is 12 + 2π.
← Didn't Know|Knew It →
What is the perimeter of a square that has an area of 81?
What is the perimeter of a square that has an area of 81?
Tap to reveal answer
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
36
A square has four equal sides and its area = side2. Therefore, you can find the side length by taking the square root of the area √81 = 9. Then, find the perimeter by multiplying the side length by 4:
4 * 9 = 36
← Didn't Know|Knew It →
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
The radius of the circle is 2 inches. What is the perimeter of the inscribed square?
Tap to reveal answer
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be .
Finally, the perimeter of a square is .
The center of an inscribed square lies on the center of the circle. Thus, the line joining the center to a vertex of the square is also the radius. If we join the center with two adjacent vertices we can create a 45-45-90 right isosceles triangle, where the diagonal of the square is the hypotenuse. Since the radius is 2, the hypotenuse (a side of the square) must be
Finally, the perimeter of a square is
← Didn't Know|Knew It →
A square table has an area of square centimeters and a perimeter of centimeters.
If , what is the perimeter of the square?
A square table has an area of
If
Tap to reveal answer
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
We start by writing the equations for the area and perimeter in terms of a side of length s.
Then, substitute both of these expressions into the given equation to solve for side length.
Finally, since four sides make up the perimeter, we substitue s back into our perimeter equation and solve for P.
← Didn't Know|Knew It →
The diagonal of square is feet. Approximately how long in inches is the perimeter of square ?
The diagonal of square
Tap to reveal answer
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that , where x is equal to the length of one side of the square.
This gives us .
Therefore, the perimeter of square is equal to .
First we must convert to inches.
The diagonal of a square divides the square into two isosceles-right triangles. Using the Pythagorean Theorem, we know that
This gives us
Therefore, the perimeter of square
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