Problem 45338. Area-04

Created by Asif Newaz

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The dimension of a rectangle is given. There are two circles of equal size that are inscribed inside it.The circles are tangent to each other and to the rectangle(on the length side).
Find the area of of the red shaded portion.
<https://serving.photos.photobox.com/46611233ca4107f77b28dc24a18635bf81510e7898924545ca289695e8891e7b898a2ae5.jpg>
Nb. I believe its more fun & ethical to try and figure out the answer by urself instead of just loooking for the ratio on the test suites.

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Last Solution submitted on Jun 02, 2024

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William on 17 Feb 2020

Asif, Thanks for another nice problem.
I think the description would be improved if it said the "red shaded portion", because there are two shaded portions in the drawing.

Christian Schröder on 19 Mar 2023

@ChrisR Going by the test suite I think the illustration should actually look like this:

clear variables
close all
[a, b] = deal(7, 2);
rectangle("Position", [-a/2 0 a b])
rectangle("Position", [-a/2 0 a/2 b], "FaceColor", "red")
rectangle("Position", [ -b 0 b b], "Curvature", [1 1], "FaceColor", "white")
rectangle("Position", [ 0 0 b b], "Curvature", [1 1])
axis equal
set(gca, "XTick", [], "YTick", [], "XColor", "w", "YColor", "w")

ChrisR on 22 Mar 2023

You're right, Christian. Thanks for correcting my comment, which I deleted.

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Problem 45338. Area-04

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