UNSW MathSoc Championship Q2

Geometry Level 2

Find the area of the region in the plane bounded by the curve 4 ∣ x ∣ + 5 ∣ y ∣ = 20 4|x|+5|y|=20 .


The answer is 40.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Tom Engelsman
Sep 22, 2017

The region in question is just a parallelogram with vertices at: ( x , y ) = ( ± 5 , 0 ) , ( 0 , ± 4 ) (x,y) = (\pm 5, 0), (0, \pm 4) . The area is just the sum of four right triangles with side lengths of 4 and 5 each ⇒ 4 ⋅ 1 2 ( 4 ) ( 5 ) = 40 . \Rightarrow 4 \cdot \frac{1}{2}(4)(5) = \boxed{40}.

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