MathDB

Problem 2

Part of 2019 LIMIT Category A

Problems(2)

cutting a square into an octagon

Source: LIMIT 2019 CAS1 P2

4/28/2021
From a square with sides of length 2m2m, corners are cut away so as to form a regular octagon. What is the area of the octagon in m2m^2? <spanclass=′latex−bold′>(A)</span> 23<span class='latex-bold'>(A)</span>~2\sqrt3 <spanclass=′latex−bold′>(B)</span> 43<span class='latex-bold'>(B)</span>~\frac4{\sqrt3} <spanclass=′latex−bold′>(C)</span> 4(2−1)<span class='latex-bold'>(C)</span>~4\left(\sqrt2-1\right) <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
geometry
computational of side lenght in quadrilateral

Source: LIMIT 2019 CAS2 P2

4/28/2021
Let ABCDABCD be a quadrilateral with sides ∣AB‾∣=2\left|\overline{AB}\right|=2, ∣BC‾∣=∣CD‾∣=4\left|\overline{BC}\right|=\left|\overline{CD}\right|=4 and ∣DA‾∣=5\left|\overline{DA}\right|=5. The opposite angles, ∠A\angle A and ∠C\angle C are equal. The length of diagonal BDBD equals <spanclass=′latex−bold′>(A)</span> 26<span class='latex-bold'>(A)</span>~2\sqrt6 <spanclass=′latex−bold′>(B)</span> 33<span class='latex-bold'>(B)</span>~3\sqrt3 <spanclass=′latex−bold′>(C)</span> 36<span class='latex-bold'>(C)</span>~3\sqrt6 <spanclass=′latex−bold′>(D)</span> 23<span class='latex-bold'>(D)</span>~2\sqrt3
geometry