Question

NO LINKS!! URGENT HELP PLEASE!!

O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary.

Answer 1

101.8 square units

Explanation:

The given diagram shows a regular octagon with a radius of 6 units.

The radius of a regular polygon is the distance from the center of the polygon to one of its vertices.

Therefore:

• Number of sides: n = 8
• Radius: r = 6

To find the area of a regular polygon given its radius and number of sides, we can use the following formula:

`\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left((180^(\circ))/(n)\right)\cos\left((180^(\circ))/(n)\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}`

Substitute n = 8 and r = 6 into the formula and solve for A:

`A=8\cdot 6^2\sin \left((180^(\circ))/(8)\right)\cos\left((180^(\circ))/(8)\right)`

`A=288\sin \left(22.5^(\circ)\right)\cos\left(22.5^(\circ)\right)`

`A=101.823376...`

`A=101.8\; \sf square\;units\;(nearest\;tenth)`

Therefore, the area of a regular octagon with a radius of 6 units is 101.8 square units, to the nearest tenth.

Answer 2

101.8 unit sqaure

Explanation:

Solution Given:

no of side(n)=8

radius(r)=6

Area =?

we have

`\boxed{\bold{Area\: of \:regular\: polygon =nr^2sin((180)/(n))Cos((180)/(n))}}`

where

r is the radius and n is no of the side.

Now

Substituting Value:

`Area\: of \:regular\: polygon =8*6^2sin((180)/(8))Cos((180)/(8))\\=8*36*0.38268*0.923879\\=101.823`

in nearest tenth 101.8 unit square