**Finding the area of a rhombus :**

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.

**Example 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.

Area of rhombus = (1/2) x (d₁ x d₂)

here, d₁ = 24 in and d₂ = 15 in

= (1/2) x 24 x 15

= 12 x 15

= 180 square inches

Hence, 180 square inches of fabric are needed to Cedric to make the kite.

**Example 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 :**

Area of rhombus = (1/2) x (d₁ x d₂)

here, d₁ = 25 in and d₂ = 15 in

= (1/2) x 25 x 15

= 187.5 square inches

**Example 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 :**

Area of rhombus = (1/2) x (d₁ x d₂)

here d₁ = 12 inches and d₂ = 16 inches

= (1/2) x 12 x 16

= 96 square inches

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

Area of parallelogram = 96

base x height = 96

10 x h = 96

h = 96/10 = 9.6 inches

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

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