The area of a rhombus is half of the product of the lengths of its diagonals.

A rhombus is a quadrilateral in which all sides are congruent and opposite sides are parallel. A rhombus can be divided into four right triangles that can then be rearranged into a rectangle.

The base of the rectangle is the same length as one of the diagonals of the rhombus. The height of the rectangle is half the length of the other diagonal.

**Problem 1 :**

Cedric is constructing a kite in the shape of a rhombus.The spars of the kite measure 15 inches and 24 inches. How much fabric will Cedric need for the kite ?

**Solution :**

To determine the amount of fabric needed, find the area of the kite.

Formula for area of a rhombus :

= ^{ }1/2 ⋅ (d_{1}d_{2})

Substitute 24 for d_{1} and 15 for d_{2}.

= ^{ }1/2 ⋅ (24 ⋅ 15)

= 12 ⋅ 15

= 180 in^{2}

So, Cedric needs 180 square inches of fabric to make the kite.

**Problem 2 :**

A kite in the shape of a rhombus has diagonals that are 25 inches long and 15 inches long. What is the area of the kite?

**Solution :**

Formula for area of a rhombus :

= ^{ }1/2 ⋅ (d_{1}d_{2})

Substitute 25 for d_{1} and 15 for d_{2}.

= ^{ }1/2 ⋅ (25 ⋅ 15)

= 1/2 ⋅ (375)

= 187.5 in^{2}

**Problem 3 :**

The diagonals of a rhombus are 12 in. and 16 in. long. The length of a side of the rhombus is 10 in. What is the height of the rhombus ?

**Solution :**

Formula for area of a rhombus :

= ^{ }1/2 ⋅ (d_{1}d_{2})

Substitute 12 for d_{1} and 16 for d_{2}.

= ^{ }1/2 ⋅ (12 ⋅ 16)

= 6 ⋅ 16

= 96 in^{2}

Because rhombus is a parallelogram, we can use the formula for area of a parallelogram to find the height of the rhombus.

Area of parallelogram = 96 in^{2 }

base x height = 96

Substitute 10 for base.

10 x h = 96

Divide each side by 10.

height = 9.6 inches

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