Question

A regular hexagon of Side 10 cm is cut from a plane circular sheet of radius 10 cm. Find the area of the remaining part of the sheet.
please answer fast!!​

Answer 1

Answer:

Area of the hexagon = 259.81.

Area of the circle = πr².

= 22/7 × 100 = 2200/7.

= 314.29

314.9 - 259.81 = 55.09.

So the area of the remaining part is 55.09 cm².

Answer 2

$\underline{\underline{\large{\pmb{\sf{Understanding\; the\; question\;:}}}}}$

Here, the concept of area related to circle has been used. We are given the side of a regular hexagon that is cut from a plane circular sheet. The radius of the circular sheet is also provided in the given question. We have been asked to calculate the area of remaining part of the sheet. In order to calculate the remaining part we firstly need to find the area of individual figure (Hexagon and circle). After finding the area we need to subtract the area of circular sheet from the area of regular hexagon.

$\underline{\underline{\large{\pmb{\sf{Formula\; used\;:}}}}}$

$\bullet\; \boxed{\bf{Area\; of\; circle=\pi\times {r}^{2}}}$

$\bullet\; \boxed{\bf{Area\; of\; hexagon=\dfrac{3\times \sqrt{3}}{2}\times {a}^{2}}}$

_______________________________________________________

$\underline{\underline{\large{\pmb{\sf{Solution\;:}}}}}$

Given,

» Side of hexagon = s = 10 cm

» Radius of the circular sheet = r = 10 cm

• FoR thE areA oF circulaR sheeT :

We know that,

$\longrightarrow\quad\sf{Area\; of\; circle=\pi\times {r}^{2}}$

Equating all the values in formula, we get:

$\longrightarrow\quad\sf{Area\; of\; circle=\dfrac{22}{7}\times {(10)}^{2}}$

Now,

$\longrightarrow\quad\sf{Area\; of\; circle=\dfrac{22}{7}\times 100}$

Performing multiplication.

$\longrightarrow\quad\sf{Area\; of\; circle=\dfrac{2200}{7}}$

Performing division.

$\longrightarrow\quad\sf{Area\; of\; circle= 314.2857\; {cm}^{2}}$

_______________________________________________________

• FoR. thE areA oF hexagoN :

We know that,

$:\implies\quad\sf{Area\; of\; hexagon=\dfrac{3\times \sqrt{3}}{2}\times {a}^{2}}$

Equating all the values in formula, we get:

$:\implies\quad\sf{Area\; of\; hexagon=\dfrac{3\times \sqrt{3}}{2}\times {10}^{2}}$

Now,

$:\implies\quad\sf{Area\; of\; hexagon=\dfrac{3\times \sqrt{3}}{2}\times 100}$

Performing division between 100 and 2.

$:\implies\quad\sf{Area\; of\; hexagon=3\times \sqrt{3}\times 50}$

Performing multiplication.

$:\implies\quad\sf{Area\; of\; hexagon=150\times \sqrt{3}}$

Now,

$:\implies\quad\sf{Area\; of\; hexagon=259.8076\; {cm}^{2}}$

_______________________________________________________

~Now, let's calculate the remaining area of the sheet. $\\\longmapsto\quad\sf{Remaining\; area=Area\; of\; circle-Area\; of\; hexagon}$

Equating all the values, we get:

$\longmapsto\quad\sf{Remaining\; area=314.2857-259.8076}$

Performing subtraction.

$\longmapsto\quad\underline{\boxed{\bold{Remaining\; area=\red{54.4781\; {cm}^{2}}}}}$

Therefore, the required answer is:

★ The area of remaining part of the sheet is 54.4781 cm².