If the region bounded by the following curves is a regular octagon, choose the correct option(s).

$∣ x ∣ + ∣ y ∣ = a, ∣ x y ∣ + 1 = ∣ x ∣ + ∣ y ∣.$

Question

If the region bounded by the following curves is a regular octagon, choose the correct option(s). ∣ x ∣ + ∣ y ∣ = a , ∣ x y ∣ + 1 = ∣ x ∣ + ∣ y ∣. ​

TestHub · Accepted Answer

The second curve is the union of the lines at unit distance from the axes. A regular octagon has equal distances from its center to all sides. The half-angle triangle gives its side length. All four options are correct.

$(∣ x ∣ - 1) (∣ y ∣ - 1) = 0. r = 1, a / 2 = r, a = 2 . s = 2 r tan (π /8) = 2 (2 - 1) . P = 8 s = 16 (2 - 1) . S = \frac{1}{2} P r = 8 (2 - 1) .$

Mathematics - Area Under Curves Question with Solution | TestHub

Options:(select one or more)

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