can you please help me find the answer

Question

Find the area of the figure.  Round to the nearest hundreth.

A=  yd²

Answer 1

The are 135 degrees in each interior angles of a regular octagon: (8-2)*180/8 = 135 degrees.

[(Number of sides - 2)*(180 degrees)/( number of sides)]

If you connect the center of the octagon to each of its vertex by a straight line, and then bisect the sides with a perpendicular, you will create 16 congruent triangles. The angles on the sides are 135/2 degrees in measure.

You can use SOH-CAH-TOA to determine the lengths ofa the sides needed to determine the area of each triangle.

The formula for each triangle is (1/2)*10*10/tan(135/2 degrees), multiplying this value by 16 yields 331.37 square yards, accurate to 2 decimal places.

Answer 2

Assuming that the figure is a regular octagon:

Draw the line joining the center to a vertex.

The angle between this line and the side is 67.5 degrees and the angle between this line and the line labeled 10 yd is 22.5 degrees.

The length of the hypotenuse of the right triangle is 10/sin 67.5

The area of the triangle is (1/2)10*(10/sin 67.5)*sin 22.5.

There are 16 such triangles.

With this information you should be able to answer the problem.