Area: Real World Problems | 6th Grade Geometry Worksheets - Free Printable

Problem: Calculate the area of the kite shown in the image.

#### Given Information:
- The kite is divided into two triangles.
- The diagonals of the kite are given:
- One diagonal (vertical) = 11 cm
- The other diagonal (horizontal) = 8 cm

#### Formula for the Area of a Kite:
The area of a kite can be calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times d_1 \times d_2
\]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

#### Step-by-Step Solution:

1. Identify the diagonals:
- \( d_1 = 11 \, \text{cm} \)
- \( d_2 = 8 \, \text{cm} \)

2. Apply the formula:
\[
\text{Area} = \frac{1}{2} \times d_1 \times d_2
\]
Substitute the values of \( d_1 \) and \( d_2 \):
\[
\text{Area} = \frac{1}{2} \times 11 \, \text{cm} \times 8 \, \text{cm}
\]

3. Perform the multiplication:
\[
\text{Area} = \frac{1}{2} \times 88 \, \text{cm}^2
\]

4. Simplify the expression:
\[
\text{Area} = 44 \, \text{cm}^2
\]

#### Final Answer:
\[
\boxed{44}
\]

Explanation:

The kite is essentially composed of two triangles that share the same diagonals. The formula for the area of a kite simplifies the calculation by using the product of the diagonals divided by 2. This method works because the diagonals of a kite bisect each other at right angles, effectively dividing the kite into four right triangles. The total area is thus half the product of the diagonals.

This approach ensures accuracy and efficiency in solving the problem.