Question

Right triangle ABF is joined to regular pentagon BCDEF at BF. We are given the following lengths:

AF = 5 ft.
AB = 12 ft.
Apothem RS = 8.95 ft.

Find the perimeter and area of both the right triangle and the pentagon.

Answer 1

A regular pentagon has equal length sides, so if you find the length of BF, you will find the length of all the other sides. BF is the hypotenuse of the right triangle ABF, so you can use Pythagorean Theorem to find its length.

RS is the height of one of the five triangles that make up the pentagon. You can find the area of one of the triangles and the rest will have the same area.

Answer 2

BF^2 = 5^2+12^2
BF^2=25+144=169
BF=13

Answer 3

omg thnk you soo much

Answer 4

The area of the triangle EFS is (b*h)/2
The base will be the same as BF, since it is a regular pentagon. The height is given, so
A = (13*8.95)/2

Once you know the area of that one triangle, multiply it by 5 to get the area of the entire pentagon.

The perimeter is just 5 times BF, of course since all the sides are equal in length.

Answer 5

You can find the perimeter of the triangle by adding up the side measurements.

The area can be found by A=(bh)/2, where b=5, h=12

Answer 6

Cheers!

Answer 7

so the answer would be 65 right?