Ask questions and get helpful responses.
Ask a New Question
  1. Questions

Math--Area

Find the area of each regular polygon to the nearest tenth. Octagon with side length of 10 kilometers.

Heres what I tried; but I don't know if im on the right track.

Area=1/2 * Perimeter* Apothem
Perimeter=base of octagon* number of sides
Perimeter=10*8=80 km.

SO A=40a
(1/2 of 80 times apothem)

How do I find the apothem of the octagon?

Work on one of the 8 triangles, since they are all equal
Such a triangle is isosceles with a 45º formed by the equal sides and the other side is 10 km.
the other two angles are 67.5º each.

The apothem, which is simply the perpendicular distance from the centre of your regular polygon to one of the sides. It becomes the height of the triangle

Let the height be h, and use trig.

tan 67.5 = x/5
x = 5 tan 67.5 = 12.071

so the area of one triangle = 1/2 * 10 * 12.071 = 60.355....
the area of the octogon is 8 times that

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
natalie

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    What is the area of the trapezoid? The diagram is not drawn to scale. 60 cm² Given the regular polygon, what is the measure of each numbered angle? m∡1 = 36°; m∡2 = 72° What are a) the ratio of the perimeters and b) the

  2. Geometry - Area

    Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth.

  3. math

    . Find the volume of the sphere with a radius of 9. Use ð = 3.14 and round your answer to the nearest tenth. 4. Find the volume of an ellipsoid with a semi-major axis of length 10 and the first semi-minor axis has length of 6

  4. Geometry

    The area of a regular octagon is 35 cm². What is the area of a regular octagon with sides three times as long?

  1. math geometry

    1. Find the missing angle measure in the figure. Graphic 140 123 121 142 2. What is the sum of the measures of the angles of a regular nonagon? What is the measure of each angle in the nonagon? 2,520°; 280° 1,440°; 160°

  2. Math

    Are the statements Always, Sometimes or Never. Please explain why. Thanks. 1. An equilateral polygon is regular. 2. The greater the number of sides of a regular polygon, the smaller the measure of any of its exterior angle. 3. The

  3. math

    1. Find the missing angle measure in the figure. Graphic 140 123 121 142 2. What is the sum of the measures of the angles of a regular nonagon? What is the measure of each angle in the nonagon? 2,520°; 280° 1,440°; 160°

  4. Geometry

    Find the area of a circle circumscribed about a regular hexagon with an apothem of 5 inches. Round to the nearest tenth

  1. math

    find the apothem, in meters, and area, in square meters, of a regular hexagon with side length 7 m. round to the nearest hundredth

  2. geometry

    The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?

  3. Algebra

    If the length of one side of a square is increased by 4 cm and the length of an adjacent side is decreased by 8 cm, the area of the figure is decreased by 20%. Find the length of each side of the square to the nearest tenth.

  4. Math

    Tell whether the pair of polygons is similar. Explain why or why not. The polygon A is bigger. The side of the polygon is 10ft and the top sides of the polygon is 11ft. The polygon B is smaller. The side of the polygon is 8.4ft

Still need help? You can ask a new question.