Question

ABCDEFGHIJ is a regular decagon with a radius of 25.89 units and a side length of 16. Find the area of ABCDEFGHIJ. Round the answer to the nearest tenth.

Answer 1

Area of the decagon is 1969.84 unit²

Explanation:

ABCDEFGHIJ is a regular decagon with radius of 25.89 units and a side length of 16.

We have to find the area of this decagon.

If we join all the diagonals of the given decagon, it will be divides in 10 triangles. Center of the decagon is point A.

In the figure attached, sides AB and AC will be equal to 25.89 and side of the decagon is 16 units.

Now we know area of decagon = 10×(Area of triangle ABC)

= 10×
`(1)/(2)(AD)(BC)`

Side AD =
`\sqrt{(25.89)^(2)-(8)^(2)}`

=
`√(670.2921-64)`

=
`√(606.2921)`

= 24.622 units

Now area of decagon = 10×(
`(1)/(2)(24.622)(16)`)

= 5×24.622×16

= 1969.84 unit²

Answer 2

A decagon is a polygon which has ten sides. A regular decagon is characterized by equal side lengths. An important dimension of this polygon is the side length. The area is expressed as:
A=(5/2)a^2(√5+(2√5))
A = (5/2)16^2(√5+(2√5))A = 1969.72