Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 4 - Section 4.3 - The Rectangle, Square, and Rhombus - Exercises - Page 195: 44

Answer

(a) $P = 4 \sqrt{5}$ (b) $P = 6\sqrt{2}$

Work Step by Step

(a) We can find the length of each side of the quadrilateral $EGIK$: $L = \sqrt{(1)^2+(2)^2}$ $L = \sqrt{1+4}$ $L = \sqrt{5}$ We can find the perimeter: $P = 4L = 4 \sqrt{5}$ (b) We can find the length of the side $EH$ of the quadrilateral $EHIL$: $L_1 = \sqrt{(2)^2+(2)^2}$ $L_1 = \sqrt{4+4}$ $L_1 = \sqrt{8}$ $L_1 = 2\sqrt{2}$ We can find the length of the side $HI$ of the quadrilateral $EHIL$: $L_2 = \sqrt{(1)^2+(1)^2}$ $L_2 = \sqrt{1+1}$ $L_2 = \sqrt{2}$ We can find the perimeter: $P = 2L_1+2L_2$ $P = (2\times 2\sqrt{2})+(2 \times \sqrt{2})$ $P = 6\sqrt{2}$
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