Question

PLEASE ANSWER QUICKLY! : There are four questions here please make sure to click through, I got the first answer from someone but they neglected to go through the photos. Oh well xD Any help is appreciated

Answer 1

Hey there :)

2 ) We know the perimeter of the regular hexagon to be 12 cm and the apothem to be
`√(3)` cm

The area formula of a regular hexagon is:
Area =
`(1)/(2)` × perimeter × apothem

Let us substitute:
A =
`( (1)/(2))(12)( √(3) )`
=
`6√(3)` cm²
Your answer will be the second option

3 ) We know the value of the apothem to be 16.9 cm and the side length to be 14 cm

The perimeter of this octagon is:
P = 8 x side
= 8 x 14
= 112 cm

Area formula of a regular octagon is
A =
`(1)/(2)` perimeter x apothem
A =
`(1)/(2)` ( 112 )( 16.9 )
= 946 .4 cm²
Your answer will be the last option

4 ) The apothem of the regular pentagon is given to be 5.5 cm and the side is 8 cm

The perimeter of this pentagon is:
P = 5 x side
= 5 x 8
= 40 cm

Area formula of a pentagon is:
Area =
`(1)/(2)` x apothem x perimeter
=
`(1)/(2)` ( 5.5 ) ( 40 )
= 110 cm²
Your answer will be the third option

5 ) The apothem of this hexagon is
`9√(3)` cm and the side is 18 cm

The perimeter of the hexagon is
P = 6 x side
= 6 x 18
= 108 cm

The area formula of a regular hexagon is
Area =
`(1)/(2)` x apothem x perimeter
=
`(1)/(2)` ( 108 )(
`9√(3)` )
= 841 cm²
Your answer will be the first option