Question

in the diagram, kl = 2√2, lm = √5, and mn = √2. what is the perimeter of isosceles trapezoid klmn? √2 units √5 units 4√2 + 2√5 units 3√2 + 2√5 units

Explanation:

Step1: Recall perimeter formula

Perimeter \(P\) of a polygon is sum of side - lengths. For trapezoid \(KLMN\), \(P = KL+LM + MN+NK\).

Step2: Use property of isosceles trapezoid

In an isosceles trapezoid, non - parallel sides are equal. Here, \(KL\) and \(MN\) are non - parallel sides and \(LM\) and \(NK\) are parallel sides. Since it is isosceles, \(NK = LM=\sqrt{5}\) and we know \(KL = 2\sqrt{2}\), \(LM=\sqrt{5}\), \(MN=\sqrt{2}\).

Step3: Calculate perimeter

\(P=KL + LM+MN+NK=2\sqrt{2}+\sqrt{5}+\sqrt{2}+\sqrt{5}\).
Combining like terms: \(P=(2\sqrt{2}+\sqrt{2})+( \sqrt{5}+\sqrt{5})=3\sqrt{2}+2\sqrt{5}\) units.

Answer:

\(3\sqrt{2}+2\sqrt{5}\) units