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Home > CCG > Chapter 12 > Lesson 12.1.2 > Problem 12-28

12-28.

Find the surface area of the solids below. Assume that the solid in part (a) is a prism with a regular octagonal base and the pyramid in part (b) is a square-based pyramid. Show all work.  

  1. An octagonal prism with a base side 4 meters and a height of 16 meters.

    Find the area of the top, and the lateral area.
    Find their sum.

    Find the measure of the central angle. Use this to find the area of the triangle. Then use the area to find the total area.

    Central Angle Measure: 

    An isosceles triangle, with base of 4. A segment, h, from the top vertex is dropped perpendicular to the base forming 2 right triangles. Top angle on left side of segment h, is 22.5 degrees.

    Area of triangle: A ?

  1. A square based pyramid with a base side 10 feet and sloping sides 13 feet.

    Use the same method you used to solve part (a).

    To find the height, draw a diagram.

    An isosceles triangle with sides, 13, and a base, 10. A line, d, from the top vertex is dropped perpendicular to the base.

    Now use the Pythagorean Theorem to find the height.
    Use that to find the area of one triangle, and then to find the total surface area.

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