Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 1 - Tools of Geometry - 1-8 Perimeter, Circumference, and Area - Lesson Check: 3

Answer

perimeter=14.8 area=10

Work Step by Step

Find the length of each side. Using the ruler postulate: top=$|-3-3|=|-6|=6$ right=$|1-(-1)|=|2|=2$ bottom=$|-1-3|=|-4|=4$ Using the distance formula, given endpoints of (-3,1) and (-1,-1): $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d=\sqrt{(-1-(-3))^2+(-1-1)^2}$ $d=\sqrt{(2)^2+(2)^2}$ $d=\sqrt{4+4}$ $d=\sqrt{8}$ $d=2.8$ Sum the lengths of the sides to find the perimeter. $P=6+2+4+2.8=14.8$ To find the area, separate the figure into a rectangle and a triangle. Use the formulas for area and substitute. Add the areas of the rectangle and triangle to find the area of the figure. The rectangle has base(b)=4 and height(h)=2. $A_1=bh=4\times2=8$ The triangle has base(b)=2 and height(h)=2. $A_2=\frac{1}{2}bh=\frac{1}{2}(2)(2)=2$ $A=A_1+A_2=8+2=10$
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