The perimeter of the hexagon ABCDEF is 93 units.
The area of the hexagon ABCDEF is 500 square units.
We have to determine
The perimeter of hexagon ABCDEF.
What is the perimeter of the hexagon?
A regular hexagon is a polygon whose all sides are equal and the regular hexagon is an equilateral triangle.
When a regular hexagon is inscribed in a circle then its side is equal to the radius of the circle.
The length of BC and CD is;
\(\rm BC = CD = \sqrt{10^2+10^2}\\\\\ BC = CD = \sqrt{100+100}\\\\ BC = CD =\sqrt{200}\\\\BC = CD =14.1421\)
And the measure of FA = EF is;
\(\rm FA = EF =\sqrt{(10^2 + 20^2)} \\\\ FA = EF =\sqrt{100+400}\\ \\ FA = EF =\sqrt{500} \\\\ FA = EF =23.3607\)
The perimeter of the hexagon is given by;
Perimeter = 10 + 10 + 14.1421 + 14.1421 + 23.3607
Perimeter = 93
The perimeter of the hexagon ABCDEF is 93 units.
And the area of the hexagon is;
The area is made up be triangle FAE, rectangle ABDE, and triangle BCD
\(\rm A = 0.5(20)(20) + (10)(20) + 0.5(20)(10)\\\\A = 500 \ square \ units\)
The area of the hexagon ABCDEF is 500 square units.
To know more about Hexagon click the link given below.
https://brainly.com/question/15362051
