How to find the length of the diagonal of a pentagon - High School Math

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Question

Find the length of the diagonal of the following pentagon:

Answer

Use the Pythagorean Theorem to find the length of the diagonal:

$(\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

$(2\ m)^2+(2.75\ m)^2 = C^2$

$C\approx 3.4\ m$

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Question

Find the length of the diagonal of the following pentagon:

Answer

Use the Pythagorean Theorem to find the length of the diagonal:

$(\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

$(3\ m)^2+(3\ m)^2=C^2$

$C=3\sqrt{2}\ m$

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