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What is the area of a region enclosed by \(|\frac{x}{3}|+|\frac{y}{9}|=10\)?
A. \(675\) B. \(1350\) C. \(2700\) D. \(5400\) E. \(10800\)
Find the \(x\) and \(y\) intercepts.
When \(y=0\), then \(x=30\) or \(x=-30\).
When \(x=0\), then \(y=90\) or \(x=-90\).
So, we have 4 points: (30, 0), (-30, 0) (0, 90), (0, -90). When joining these points we get the rhombus:
The area of a rhombus is \(\frac{d_1*d_2}{2}\) (where \(d_1\) and \(d_2\) are the lengths of the diagonals), thus the area of the enclosed figure is \(\frac{60*180}{2}=5,400\).
More reliable way to find out whether this is square or not is to know the fact that, when the Rise/Run is equal i.e 10/10 or 25/25 in otherwords where the Slope is 1, we end up with 45-45-90 triangle. we add up all the four 45-45-90 triangle we end up with square, in this example clearly the Rise/Run is not 1. Hence it is a Rhombus and not a square.
In case you don't have the equation for the area of a rhombus memorized, you could have also multiplied the area of a triangle by 4. This figure is made up of 4 equal triangles. Area of triangle = 1/2bh Area of our figure=4*(1/2*30*90)=5400 Answer=D.
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48% (01:13) correct 
