# High School Math : Quadrilaterals

## Example Questions

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### Example Question #1 : Quadrilaterals

What is the area of a kite with diagonals of 5 and 7?

Explanation:

To find the area of a kite using diagonals you use the following equation

That diagonals ( and )are the lines created by connecting the two sides opposite of each other.

Plug in the diagonals for  and  to get

Then multiply and divide to get the area.

### Example Question #2 : Quadrilaterals

Find the area of the following kite:

Explanation:

The formula for the area of a kite is:

Where  is the length of one diagonal and  is the length of the other diagonal

Plugging in our values, we get:

### Example Question #3 : Quadrilaterals

Find the area of the following kite:

Explanation:

The formula for the area of a kite is:

where  is the length of one diagonal and  is the length of another diagonal.

Use the formulas for a  triangle and a  triangle to find the lengths of the diagonals. The formula for a  triangle is  and the formula for a  triangle is .

Our  triangle is:

Our  triangle is:

Plugging in our values, we get:

### Example Question #1 : How To Find The Perimeter Of Kite

Find the perimeter of the following kite:

Explanation:

In order to find the length of the two shorter edges, use a Pythagorean triple:

In order to find the length of the two longer edges, use the Pythagorean theorem:

The formula of the perimeter of a kite is:

Plugging in our values, we get:

### Example Question #5 : Quadrilaterals

Find the perimeter of the following kite:

Explanation:

The formula for the perimeter of a kite is:

Where  is the length of the longer side and  is the length of the shorter side

Use the formulas for a  triangle and a  triangle to find the lengths of the longer sides. The formula for a  triangle is  and the formula for a  triangle is .

Our  triangle is:

Our  triangle is:

Plugging in our values, we get:

### Example Question #1 : Trapezoids

The following quadrilaterals are similar. Solve for .

(Figure not drawn to scale).

Explanation:

When polygons are similar, the sides will have the same ratio to one another. Set up the appropriate proportions.

Cross multiply.

### Example Question #7 : Quadrilaterals

Find the area of the following trapezoid:

Explanation:

The formula for the area of a trapezoid is:

Where  is the length of one base,  is the length of the other base, and  is the height.

To find the height of the trapezoid, use a Pythagorean triple:

Plugging in our values, we get:

### Example Question #8 : Quadrilaterals

Find the area of the following trapezoid:

Explanation:

Use the formula for  triangles in order to find the length of the bottom base and the height.

The formula is:

Where  is the length of the side opposite the .

Beginning with the  side, if we were to create a  triangle, the length of the base is , and the height is .

Creating another  triangle on the left, we find the height is , the length of the base is , and the side is .

The formula for the area of a trapezoid is:

Where  is the length of one base,  is the length of the other base, and  is the height.

Plugging in our values, we get:

### Example Question #9 : Quadrilaterals

Determine the area of the following trapezoid:

Explanation:

The formula for the area of a trapezoid is:

,

where  is the length of one base,  is the length of another base, and  is the length of the height.

Plugging in our values, we get:

### Example Question #10 : Quadrilaterals

Find the area of the following trapezoid:

Explanation:

The formula for the area of a trapezoid is:

,

where  is the length of one base,  is the length of another base, and  is the length of the height.

Use the Pythagorean Theorem to find the height of the trapezoid:

Plugging in our values, we get:

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