Kite Area Calculator

What is a Kite?

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal. The diagonals of a kite intersect at right angles.

Formulas for Kites

Let \(d_p\) be the length of the first diagonal, \(d_q\) be the length of the second diagonal, \(A\) be the area, and \(P\) be the perimeter. Then:

1. Area: \(A = \frac{d_p \times d_q}{2}\)
2. Perimeter: \(P = 2 \times \sqrt{\left(\frac{d_p}{2}\right)^2 + \left(\frac{d_q}{2}\right)^2}\)

Step-by-Step Calculations

Let's calculate these properties for a kite with diagonals \(d_p = 10\) units and \(d_q = 8\) units:

1. Area: \[A = \frac{d_p \times d_q}{2} = \frac{10 \times 8}{2} = 40 \text{ square units}\]
2. Perimeter: \[P = 2 \times \sqrt{\left(\frac{d_p}{2}\right)^2 + \left(\frac{d_q}{2}\right)^2} = 2 \times \sqrt{\left(\frac{10}{2}\right)^2 + \left(\frac{8}{2}\right)^2} = 2 \times \sqrt{25 + 16} = 2 \times \sqrt{41} = 12.81 \text{ units}\]

Visual Representation