Question

the perimeter of a regular pentagon is 1540 cm how long is each side? if the pentagon is divided into 5 equal triangles, how much area would each cover?

Answer 1

Answer:

Addition of all Sides of Given figure is called perimeter

Perimeter of the regular pentagon

⇒5×length of sides=1540 cm

⇒ length of sides =

4

1540

cm=308 cm

∴ Length of the side of the regular pentagon is 308 cm

Answer 2

$\huge\underline{\bf{Given}}$

• Perimeter of a regular pentagon = 1540 cm

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$\huge\underline{\bf{To\: find}}$

• Each side of the pentagon.
• Area cover by each triangle if the pentagon is divided into 5 equal triangles.

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$\huge\underline{\bf{Concept}}$

※ This question is related to our understanding capacity. The concept is very clear that firstly we have to find the side of the pentagon. Since, it is a regular pentagon so it's all sides are equal.

⠀

$\huge\underline{\bf{Solution}}$

• Let the side of the pentagon be x.

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$\: \: \: \: \: \: \: \boxed{\bf{\bigstar{Perimeter\: of\: pentagon = 5x{\bigstar}}}}$

$\tt\longmapsto{5x = 1540}$

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$\tt\longmapsto{x = \dfrac{1540}{5}}$

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$\tt\longmapsto{x = 308}$

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Now,

• Let the area of the pentagon be A.

⠀

Since, we have to divide it into five equal triangles.

$\boxed{\bf{\bigstar{5 \times \: Area\: of\: one\: triangle = Area\: of\: pentagon{\bigstar}}}}$

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$\tt:\implies{5 \times Area\: of\: one\: triangle = A}$

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$\tt:\implies{Area\: of\: one\: triangle = \dfrac{1}{5} A}$

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★ Hence, each triangle covers ⅕th part of the whole area.

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