### All HSPT Math Resources

## Example Questions

### Example Question #49 : Geometry

What is the circumference of a circle with a radius of 5?

**Possible Answers:**

**Correct answer:**

The formula for circumference is or .

Since we are given the radius, we will use .

### Example Question #1 : How To Find The Perimeter Of A Figure

What is the perimeter of a square with a side length of 4?

**Possible Answers:**

**Correct answer:**

The formula for the perimeter of a square is , where is the length of one side of the square.

So

### Example Question #2 : How To Find The Perimeter Of A Figure

If the perimeter of a rectangle is 40, and the width of the rectangle is 8, what is the length of the rectangle?

**Possible Answers:**

**Correct answer:**

The formula for the perimeter of a rectangle is , where is the length of the rectangle and is the width.

Plug in the numbers that we are given into the equation.

### Example Question #3 : How To Find The Perimeter Of A Figure

What is the perimeter of a rectangle with a base of 4 and a height of 8?

**Possible Answers:**

**Correct answer:**

When searching for the perimeter of a rectangle we are looking for the sum of the lengths of all of the sides enclosing the figure. In this case there are four sides, two that are the base and two that are the height. To find the perimeter we add all four of them together.

Therefore the equation for the perimeter of a rectangle is

In this case the equation looks like this

Multiply the numbers together

Then add them to get the answer

### Example Question #4 : How To Find The Perimeter Of A Figure

What is the height of a rectangle with a perimeter of 30 and base of 12?

**Possible Answers:**

**Correct answer:**

The perimeter of a rectangle is the sum of four sides, two that are the base and two that are the height. To find the perimeter we add all four of them together.

Therefore the equation for the perimeter of a rectangle is

In this example we plug in the base and the perimeter so the equation looks like this

Perform the multiplication to get

Subtract from both sides to arrive at

Then divide by 2 to find the height

The answer

### Example Question #5 : How To Find The Perimeter Of A Figure

What is the perimeter of a square with a side legnth of 8?

**Possible Answers:**

**Correct answer:**

When searching for the perimeter of a square we are looking for the sum of the lengths of all of the sides enclosing the figure. In this case there are four sides that are all equal length. To find the perimeter we add all four of them together or multiply the side length by four.

In this example the equation looks like this:

Multiply the numbers together to get .

### Example Question #6 : How To Find The Perimeter Of A Figure

What is the radius of a circle with a circumference of ?

**Possible Answers:**

**Correct answer:**

To find the radius of a circle given the circumference we must first know the equation for the circumference of a circle which is

Then we plug in the circumference into the equation for yielding

We then divide each side by :

We then have the answer for which is .

### Example Question #1 : Rectangles

A rectangular garden has an area of . Its length is meters longer than its width. How much fencing is needed to enclose the garden?

**Possible Answers:**

**Correct answer:**

We define the variables as and .

We substitute these values into the equation for the area of a rectangle and get .

or

Lengths cannot be negative, so the only correct answer is . If , then .

Therefore, .

### Example Question #7 : How To Find The Perimeter Of A Figure

What is the perimeter of a square with a diagonal of ?

**Possible Answers:**

**Correct answer:**

To find the perimeter of the square, find the length of the side. Write the formula to find the length of the side.

Substitute the diagonal and solve for the side.

First, square each side to get rid of the square root.

Divide 2 by each side to isolate the

Take the square root of each side.

Since there are four sides in a square, multiply the side length by four to get the perimeter.

### Example Question #8 : How To Find The Perimeter Of A Figure

An equilateral triangle has a length of . What is the perimeter?

**Possible Answers:**

**Correct answer:**

The perimeter of an equilateral triangle is three times the length of its side.