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Crank
2 years ago
14

Calculate the area of the square shown below (HARD)

Mathematics
1 answer:
sergey [27]2 years ago
7 0
Check the picture below.

recall that in a square, all sides are equal, so if we make b = a, then we get that for one side, also recall that the area of a rectangle is length*width, so in this case,

\bf \stackrel{\textit{area of the square}}{\stackrel{length}{5\sqrt{2}}\cdot \stackrel{width}{5\sqrt{2}}}\implies 25(\sqrt{2})^2\implies 25\cdot 2\implies 50

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Unghiurile ∢AOB, ∢BOC, ∢COD și ∢DOA sunt unghiuri în jurul punctului O, ∢AOB = 80°, ∢BOC = 140° și CO ⊥ OD.
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a) ∡AOC = 140 °

∡AOD = 40 °

b) ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC (unghiuri formate din segmentul OC) prin urmare, segmentul OC bisectează ∡AOB

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a) Calculați măsurile unghiurilor ∢AOC și ∢AOD.

b) Arătați că jumătatea liniei opuse jumătății liniei OC este bisectoarea unghiului ∢AOB

a) Parametrii dați sunt;

∡AOC. ∡BOC. ∡COD și ∡DOA sunt unghiuri în jurul circumferinței unui cerc

∡AOB = 80 ° și ∡BOC = 140 °, segmentul CO este perpendicular pe segmentul DO

Prin urmare, avem;

∡AOB + ∡BOC + ∡AOC = 360 ° (Suma unghiurilor într-un punct = 360 °)

∴ ∡AOC = 360 ° - (∡AOB + ∡BOC) = 360 ° - (80 ° + 140 °) = 140 °

  ∡AOC = 140 °

∡BOC + ∡BOD = 180 ° (Suma unghiurilor unui triunghi = 180 °)

∡BOD = 180 ° - ∡BOC = 180 ° - 140 ° = 40 °

∡BOD = 40 °

∡ BOD + ∡AOD = ∡AOB

∡AOD = ∡AOB - ∡BOD = 80 ° - 40 ° = 40 °

∡AOD = 40 °

b) Deoarece avem ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC = 140 °, avem;

∡AOB = 140 ° + 140 ° = 280 ° = 2 × ∡BOC = 2 × ∡AOC

Prin urmare, segmentul OC bisectează ∡AOB

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