# Geometry

posted by .

Find the surface area of a right octagonal pyramid with height 2.5 yards, and its base has apothem length 1.5 yards.

• Geometry -

The surface area is equal to the area of the base plus the area of the 8
isosceles triangles on the sides.The base consist of 8 isosceles triangles
also.

A = Ab + A(sides).

Ac = 360/N = 360/8 = 45Deg = central angle.

Base angles = (180 - 45) / 2 = 67.5deg
each.

tan67.5 = h/(b/2) = 1.5/(b/2),
b/2 = 1.5 / tan67.5 = 0.62,
b = 2 * 0.62 = 1.24yds = base of each
triangle.

Ab = (b*h/2)N = (1.24*1.5/2)8 = 7.44sq
yds.

Area of Sides:
Altitude = 2.5*sin67.5 = 2.31YDS.

Area of sides = (b*h/2)N =
(1.24*2.31/2)8 = 11.5 sq. yds.

Surface Area = 7.44 + 11.5 = 18.9 sq yds.

• Geometry -

CORRECTION!

Area of the sides:
The height(altitude) is GIVEN: 2.5 yds.

S = h/sin67.5 = 2.5 / sin67.5 - 2.71
yds = length of each side.

As = (b*h/2)N = (1.24*2.5/2)8 = 12.4sq yds.= Area of sides.

Surface Area = Ab + As = 7.44 + 12.4
= 19.84sq yds.

## Similar Questions

1. ### geometry

The limestone blocks from which an ancient pyramid was made weigh about 2 tons per cubic yard. Find the approximate weight of the pyramid having a square base of length 250 yards and a height of 150 yards.
2. ### geometry

Pyramid has a base 6 yards X 6yards. Its height is 4 yards. Volume= Surface Area= I got 60 square yards for the surface area but it was wrong.
3. ### math

looking at a square pyramid, if the size of the base remains the same and the height of the pyramid varies what are the minimum surface area and minimum volume the pyramid can have?
4. ### geometry

a right squarepyramid has a base length of 4cm and heeight of 10cm.how many times greater is the surface area of a right square pyramid with the same height if the base length is doubled?
5. ### Math

Find the surface area of a right octagonal pyramid with height 2.5 yards, and its base has apothem length 1.5 yards.
6. ### algebra

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the linger base to be 7 yards greater than the height. She wants the area to be 295 square …
7. ### GEOMETRY (SA oftriangular pyramid)

Find the surface area of a triangular pyramid with b =4 cm, h= 8.2 cm and s = 7 cm. PLEASE. How ?
8. ### 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.
9. ### algebra 2

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 295 square …