# Advanced Geometry : Kites

## Example Questions

### Example Question #3 : How To Find The Area Of A Kite

Two congruent equilateral triangles with sides of length  are connected so that they share a side. Each triangle has a height of . Express the area of the shape in terms of .

Explanation:

The shape being described is a rhombus with side lengths 1. Since they are equilateral triangles connected by one side, that side becomes the lesser diagonal, so .

The greater diagonal is twice the height of the equaliteral triangles, .

The area of a rhombus is half the product of the diagonals, so:

### Example Question #4 : How To Find The Area Of A Kite

Find the area of a kite if the diagonal dimensions are  and .

Explanation:

The area of the kite is given below.  The FOIL method will need to be used to simplify the binomial.

### Example Question #5 : How To Find The Area Of A Kite

The diagonal lengths of a kite are  and . What is the area?

Explanation:

The area of a kite is given below. Substitute the given diagonals to find the area.

### Example Question #6 : How To Find The Area Of A Kite

Find the area of a kite if the length of the diagonals are  and .

Explanation:

Substitute the given diagonals into the area formula for kites. Solve and simplify.

### Example Question #7 : How To Find The Area Of A Kite

The diagonals of a kite are  and . Find the area.

Explanation:

The formula for the area for a kite is

, where  and  are the lengths of the kite's two diagonals. We are given the length of these diagonals in the problem, so we can substitute them into the formula and solve for the area:

### Example Question #8 : How To Find The Area Of A Kite

The diagonals of a kite are  and . Express the kite's area in simplified form.

Explanation:

Write the formula for the area of a kite.

Substitute the diagonals and reduce.

Multiply the parenthetical elements together by distributing the :

You can consider the outermost fraction with  in the denominator as multiplying everything in the numerator by :

Change the added  to  to create a common denominator and add the fractions to arrive at the correct answer:

### Example Question #9 : How To Find The Area Of A Kite

If the diagonals of a kite are  and , express the area in simplified form.

Explanation:

Write the formula for the area of a kite:

Substitute the given diagonals:

Distribute the :

Create a common denominator for the two fractions in the numerator:

You can consider the outermost division by  as multiplying everything in the numerator by :

Multiply across to arrive at the correct answer:

### Example Question #10 : How To Find The Area Of A Kite

Find the area of a kite if one diagonal is  long, and the other diagonal is  long.

Explanation:

The formula for the area of a kite is

Plug in the values for each of the diagonals and solve.

### Example Question #11 : How To Find The Area Of A Kite

Find the area of a kite with the diagonal lengths of  and .

Explanation:

Write the formula to find the area of a kite.  Substitute the diagonals and solve.

### Example Question #12 : How To Find The Area Of A Kite

Find the area of a kite with diagonal lengths of  and .