### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #1 : Quadrilaterals

Use this image for the following problem.

What is the perimeter of the square in this picture?

**Possible Answers:**

**Correct answer:**

The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles.

Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.

Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take because a square has 4 sides.

Our perimeter is .

### Example Question #1 : Quadrilaterals

Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up feet of border, what is the length of one wall?

**Possible Answers:**

**Correct answer:**

When Sandy puts the border around her son's room, she will need enough to cover the perimeter. Since the room has four walls equal in length, we know that the room is a square. The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4. This can be written as:

Since we know that Sandy used feet of border, we know the perimeter is . We can now write an equation:

Now, in order to isolate the variable, we can divide both sides by four.

The left-hand side simplifies to:

The right-hand side simplifies to:

When we solve, we find that the length of each wall is .

### Example Question #1 : Quadrilaterals

Find the perimenter:

**Possible Answers:**

**Correct answer:**

The perimeter is equal to the sum of the length of all sides. Each side is equal to . Therefore, the perimeter equals:

### Example Question #4 : Quadrilaterals

Find the perimeter of a square with side length 10.

**Possible Answers:**

**Correct answer:**

To solve, simply multiply the side length by 4 since all sides in a square area equal. Thus,

### Example Question #5 : Quadrilaterals

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the perimeter of the building?

**Possible Answers:**

**Correct answer:**

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the perimeter of the building?

To find the perimeter of a square, we need to multiply the side length by 4.

Our side length is mile, so do the following to find our answer:

So the perimeter is

### Example Question #6 : Quadrilaterals

Use the following to answer the question.

Find the perimeter of the square.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a square, we use the following formula:

where *a, b, c, *and *d* are the lengths of each side.

Now, we know that a square has equal sides. So given the square

we know that each side equals 6ft. So, we can use this to substitute into the formula. We get

### Example Question #7 : Quadrilaterals

Find the perimeter of a square with a width of 8 inches.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a square, we use the following formula:

where *a, b, c*, and *d* are the lengths of the sides of the square.

Now, we know the width of the square is 8 inches. Because it is a square, we know all sides are equal. Therefore, all sides are 8 inches. Knowing this, we can substitute into the formula. We get

### Example Question #8 : Quadrilaterals

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the perimeter of one of its surfaces?

**Possible Answers:**

Cannot be determined from the information provided.

**Correct answer:**

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the perimeter of one of its surfaces?

Begin by realizing that we need to find the perimeter of a square.

Next, recall that the height of a cube is the same as its length and width. In other words, one surface of a cube will be a square with sides equal to the height of the cube.

Armed with this knowledge, we can find the perimeter of the square.

So our answer is 8cm

### Example Question #9 : Quadrilaterals

A square stamp has an edge length of 6 centimeters, what is its perimeter?

**Possible Answers:**

**Correct answer:**

A square stamp has an edge length of 6 centimeters, what is its perimeter?

To find the perimeter of a square, we simply can multiply the edge length by 4.

Doing so yields:

### Example Question #10 : Quadrilaterals

Find the perimeter of a square that has a base of length 9 inches.

**Possible Answers:**

**Correct answer:**

To find the perimeter of a square, we will use the following formula:

where *a, b, c, *and *d* are the lengths of each side of the square.

Now, we know the base has a length of 9 inches. Because it is a square, we know that all sides are equal. Therefore, all sides are 9 inches. Knowing this, we can substitute into the formula. We get

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