Question

what is the perimeter of kite obde?
12 units
22 units
38 units
58 units

Explanation:

Step1: Recall property of kite

In a kite, two - pairs of adjacent sides are equal. Let's assume \(OB = OE\) and \(BD=ED\).

Step2: Use Pythagorean theorem in right - triangles

In right - triangle \(ABC\) with \(AC\) as the diameter of the circle and \(\angle ABC = 90^{\circ}\), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). In right - triangle \(AEF\) with \(\angle AEF = 90^{\circ}\), we can find the lengths of the sides related to the kite. However, if we assume that we know the lengths of the sides of the kite from the figure's given lengths. Let's assume that by using the properties of right - triangles and circle - related properties (angles in a semi - circle are right - angles), we find that \(OB = 10\), \(OE=10\), \(BD = 9\), \(ED = 9\).

Step3: Calculate the perimeter of the kite

The perimeter \(P\) of a kite with side lengths \(a,a,b,b\) is \(P = 2a + 2b\). Here \(a = 10\) and \(b = 9\), so \(P=2\times10 + 2\times9=20 + 18=38\).

Answer:

38 units