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Kite_series_2

Using the kite shown above, find the length of side

Explanation

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Thus, the length of side .

Since, , must equal .

Kite_series_2

Using the kite shown above, find the length of side

Explanation

A kite is a geometric shape that has two sets of equivalent adjacent sides.

Thus, the length of side .

Since, , must equal .

A kite has an area of square units, and one diagonal is units longer than the other. In unites, what is the length of the shorter diagonal?

Explanation

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$119=\frac{x(x+3)}{2}$

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, .

The length of the shorter diagonal is units long.

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

Explanation

Write the formula for the area of a kite.

$A= \frac{d1\cdot d2}{2}$

Plug in the given diagonals.

$A= \frac{(a+b)\cdot (2a-2b)}{2}$

Pull out a common factor of two in and simplify.

$A= \frac{(a+b)\cdot2(a-b)}{2}$

Use the FOIL method to simplify.

A kite has a perimeter of inches. One pair of adjacent sides of the kite have a length of inches. What is the measurement for each of the other two sides of the kite?

$\frac{7}{2}in$

$\frac{6}{5}in$

Explanation

To find the missing side of this kite, work backwards using the formula:

, where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

$\frac{26}{2}=(6+b)$

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 .

$\frac{h}{2}$

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:

$A=\frac{pq}{2}=\frac{1 \cdot 2h}{2}=h$

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 .

$\frac{h}{2}$

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:

$A=\frac{pq}{2}=\frac{1 \cdot 2h}{2}=h$

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

Explanation

Write the formula for the area of a kite.

$A= \frac{d1\cdot d2}{2}$

Plug in the given diagonals.

$A= \frac{(a+b)\cdot (2a-2b)}{2}$

Pull out a common factor of two in and simplify.

$A= \frac{(a+b)\cdot2(a-b)}{2}$

Use the FOIL method to simplify.

A kite has an area of square units, and one diagonal is units longer than the other. In unites, what is the length of the shorter diagonal?

Explanation

Let be the length of the shorter diagonal. Then the length of the longer diagonal can be represented by .

Recall how to find the area of a kite:

$\text{Area}=\frac{(\text{Diagonal 1})(\text{Diagonal 2})}{2}$

Plug in the given area and solve for .

$119=\frac{x(x+3)}{2}$

Since we are dealing with geometric shapes, the answer must be a positive value. Thus, .

The length of the shorter diagonal is units long.

A kite has a perimeter of inches. One pair of adjacent sides of the kite have a length of inches. What is the measurement for each of the other two sides of the kite?

$\frac{7}{2}in$

$\frac{6}{5}in$

Explanation

To find the missing side of this kite, work backwards using the formula:

, where and represent the length of one side from each of the two pairs of adjacent sides.

The solution is:

$\frac{26}{2}=(6+b)$

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