Mathematics: 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.

she could get the thing she lostExplanation:...

Abcdefghij is a regular decagon with a radius of

Gearyjames8

09.01.2022

Area of the decagon is 1969.84 unit²

Step-by-step 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× $\frac{1}{2}(AD)(BC)$

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

= $\sqrt{670.2921-64}$

= $\sqrt{606.2921}$

= 24.622 units

Now area of decagon = 10×( $\frac{1}{2}(24.622)(16)$ )

= 5×24.622×16

= 1969.84 unit²

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