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? asked in Science & MathematicsMathematics · 6 years ago

I need some geometry help.?

I took a test and want to know how I got some of them wrong. I need the work.

Find the area of a pentagon with side length 20.

Answer=688

3 Answers

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  • DWRead
    Lv 7
    6 years ago

    Draw a picture.

    Divide the pentagon radially into five identical isosceles triangles with vertex angle = 72° and base angles of 54°.

    Height of triangle = 10tan(54°)

    Find the area of a triangle and multiply it by five.

    Attachment image
  • Thomas
    Lv 7
    6 years ago

    A=ns^2/(4tan(180/n)) for regular polygons for any n sides ≥ 3

    In this case s=20 and n=5 so

    A=2000/(4tan(36))=688.19

  • ted s
    Lv 7
    6 years ago

    hint : a pentagon {regular } has 5 congruent isoceles triangles with angles { 72° , 54° , 54° }...each with base 20 and height 10 tan 54°

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