# ISEE Upper Level Math : Quadrilaterals

## Example Questions

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### Example Question #1 : How To Find An Angle In Other Quadrilaterals

Three of the interior angles of a quadrilateral measure , and . What is the measure of the fourth interior angle?

Explanation:

The measures of the angles of a quadrilateral have sum . If  is the measure of the unknown angle, then:

The angle measures .

### Example Question #2 : How To Find An Angle In Other Quadrilaterals

The angles of a quadrilateral measure . Evaluate .

Explanation:

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for  in the equation:

### Example Question #1 : Quadrilaterals

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and  degrees. What is the value of ?

Explanation:

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

### Example Question #4 : How To Find An Angle In Other Quadrilaterals

In a quadrilateral, the angles have the following values:

What is the value of ?

Explanation:

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

### Example Question #1 : How To Find The Length Of The Side Of Other Quadrilaterals

The perimeter of a quadrilateral is 86. The four sides measure

.

What is the value of ?

Explanation:

Given that the perimeter is 86, the sides of the quadrilateral will all add up to this amount.

The first step is the add together all the integers.

Next, we subtract 70 from each side.

We reduce the left side of the equation:

Now, we divide each side by 4. This leaves:

### Example Question #1 : Squares

Side  shown below in square  is equal to 17.5 inches. What is the perimeter of ?

Cannot be determined

Explanation:

The perimeter of a quadrilateral is the sum of the length of all four sides. In a square, each side is of equal length. Thus, the perimeter is the length of a side (given) times 4.

### Example Question #1 : Quadrilaterals

If the area of a square is , what is the perimeter?

Explanation:

If the area of a square is , then the length of one side will be equal to the square root of

The perimeter is equal to 4 times the length of one side.

This gives us:

### Example Question #232 : Plane Geometry

If one of the edges has a length of 6 inches, what is the perimeter of one side of the box?

Explanation:

If one of the edges has a length of 6 inches, what is the perimeter of one side of the box?

To find perimeter of a square, simply multiply the side length by 4

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

In the above diagram, the circle is inscribed inside the square. The circle has circumference 30. What is the perimeter of the square?

Explanation:

Call the diameter of the circle . The length of each side of the square also is equal to this.

The diameter of the circle is equal to its circumference divided by , so

.

The perimeter of the square is four times this sidelength, so

.

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

Find the perimeter of a square with a width of 4cm.

Explanation:

To find the perimeter of a square, we will 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 has a length of 4cm.  Because it is a square, all sides are equal.  Therefore, all sides are 4cm.

Knowing this, we can substitute into the formula.  We get

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