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Analytic Geometry

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A triangular region is enclosed by the lines with equations y = 1/2 x + 3, y = -2x + 6 and y = 1. What is the area of the triangular region? Express your answer as a decimal to the nearest hundredth.

Thank you!

Jun 15, 2018

#1
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Hi,

Have you tried doing a rough graph?

I'd find the 3 points of intection, they are your vertices.

Y=1 is a horizontal line, I'd would use that as the base.  The length of this side will be easy to find.

The height from this line is also very easy to get.

Then just use the area of a triangle formula  half*base*height Jun 15, 2018
#2
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Ok, so here's my graph:

https://www.desmos.com/calculator/dgobto8opj

The equation I have been told for area calculations is [(h_b)b]/2 which gave me an area of 16.9 which is incorrect.  For your method, what does "half" refer to?

Thanks!

AnonymousConfusedGuy  Jun 15, 2018
#3
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Using your graph, I get 8.45 units ^2     (did you forget to multiply by 1/2 ?)

1/2 x b x h = area

ElectricPavlov  Jun 15, 2018
edited by Guest  Jun 15, 2018
edited by Guest  Jun 15, 2018
#4
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You were right! My bad, thanks!

AnonymousConfusedGuy  Jun 15, 2018
#5
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What is the area of the triangular region? Express your answer as a decimal to the nearest hundredth.    Jun 15, 2018