Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #133 : How To Find The Area Of A Square

Square A has an area of . The sides of Square B are triple the size of the sides of Square A. What is the area of Square B?

Possible Answers:

Correct answer:

Explanation:

Because the area of Square A is , and the formula for the area of a square is , we simply plug it in, as follows:

So the length of Square A's sides is . In order to get the length of Square B's sides, we must multiply this by , which gives us .

We then plug this into the formula for area:

Example Question #135 : How To Find The Area Of A Square

What is the area of a square that has side lengths of 4 inches?

Possible Answers:

Correct answer:

Explanation:

To find the area of a square you must know that a square has four sides and all sides are the same length. The formula for finding the area of a square is the length multiplied by the width, or .

The length times width in this case would be .

When answering an area question the answer must be put in units squared, or . In this case it would be inches squared, or .

Therefore the answer is 

Example Question #821 : Basic Geometry

What is the area of a square that has side lengths of 10 inches?

Possible Answers:

Correct answer:

Explanation:

To find the area of a square you must know that a square has four sides and all sides are the same length. The formula for finding the area of a square is the length multiplied by the width, or .

The length times width in this case would be .

When answering an area question the answer must be put in units squared, or . In this case it would be inches squared, or .

Therefore the answer is 

Example Question #412 : Quadrilaterals

One of the sides of a square has a length of . The perimeter of the square is 4 times larger than one side of the square. What is the area of the square?

Possible Answers:

There is not enough information given.

Correct answer:

Explanation:

The formula for the area of a square is , with  being one side of the square. Since we know one side is , we simply plug this in to get the area, as follows:

.

*Note that while the statement about perimeter is true (and always will be, since the formula for the perimeter of a square is ), this statement is not needed to solve the problem. 

Example Question #822 : Basic Geometry

A cube has a side length of 5 inches. What is the total surface area of all its faces?

Possible Answers:

None of these.

Correct answer:

Explanation:

A cube has 6 faces with congruent squares. Since the length of one edge is 5 inches, the area of that face is .

Multiply this by the 6 faces present to get  .

Example Question #822 : Plane Geometry

Rec 8

Find the area of the square.

Possible Answers:

Correct answer:

Explanation:

To find the area of the square, use the equation 

 

or 

.  

For a square, the base and height are the same so to find the area, you can multiply one side by itself.  

In the case of this problem, the base is .  

When we square this value, the area of the square is 

Example Question #822 : Plane Geometry

Rec 9

If the area of the square is , find the length of one side of the square.

Possible Answers:

Correct answer:

Explanation:

To find the length of one side, we have to work backwards using the formula to find the area of a square.  

That formula is 

.  

Since we know the area is , we can plug that into the equation and solve for .  

Take the square root of  to find .  

This means that our final answer is  and that is the length of one side of the square.

Example Question #822 : Plane Geometry

6 square

Find the area of the square.

Possible Answers:

Correct answer:

Explanation:

To find the area of the square, use the same formula: 

.  

Although the base is a radical, we can still use this formula.  When we multiply two radicals, we multiply the value under the radical and take the root of that.  In other words, we have to multiply 6 by 6 and take its square root.  

This means we take the square root of 36, which is 6.  Another way, when you multiply two square roots that are the same, the roots cancel and you get the value that is under the radical.  Therefore, the area of the square is .

Example Question #823 : Plane Geometry

Other square cool

Find the area of the square.

Possible Answers:

Correct answer:

Explanation:

To find the area of the square, use the equation 

 

or 

.  

For a square, the base and height are the same so to find the area, you can multiply one side by itself.  

In the case of this problem, the base is .  

When we square this value, the area of the square is .

Example Question #824 : Plane Geometry

Last rec

Find the area of the square.

Possible Answers:

Correct answer:

Explanation:

To find the area of the square, use the equation 

 

or 

.  

For a square, the base and height are the same so to find the area, you can multiply one side by itself.  

In the case of this problem, the base is .  

When we square this value, the area of the square is .

Learning Tools by Varsity Tutors