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find the surface area that a best octagonal pyramid v 0 votes
height 2.5 yards, and its base has apothem length 1.5 yardspyramid-surfaceareaaskedJun 14, 2013in ALGEBRA 2by futaiScholar
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The pyramid consists of an octagonal base and also eight isosceles triangles.
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Let the center of the basic be A. Any type of apothem will meet a side of the octagon in ~ the midpoint of the side.
Let that midpoint it is in B. Permit one end of the side be C.
Then alphabet is a right-angled triangle. It is just one of 16 comparable triangles making up the octagon.
The edge CAB = 2pi/16 = pi/8
octagonal pyramid apothem size is ab = 1.5 yards
So CB = 1.5 tan (pi/8)
Apply half-angle formula tan (a/2) = (1-cos a)/sin a
tan (pi/8) = <1-cos(pi/4)>/sin (pi/4)
= <1- (1/√2)/(1/√2)
Substitute tan (pi/8) = √2 -1
CB = 1.5 (√2 -1)
So base area = 16 x 1.5 x 1.5(√2 - 1) x (1/2)
= 18(√2 - 1)
= 7.456 sq. Yds. (approx.)
Now, permit the optimal of the pyramid be D.
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octagonal pyramid with height 2.5 yards
BD = √<(2.5)^2+(1.5)^2>
The full area that the sloping deals with of the pyramid = 8 x √(8.5) x (1.5) x (√2 - 1)
= 6 √34 (√2 - 1)
= 14.492 sq. Yds. (approx.)
If you are counting the base, total area the pyramid = 18(√2 - 1)+ 6 √34 (√2 - 1)
= (18 + 6 √34)(√2 - 1)
= 6(3 +√34 )(√2 - 1)
= 21.948 sq. Yds. (approx.).answeredJul 5, 2013by goushiPupil please log in or it is registered to add a comment. related questionsIn a square pyramid, the perimeter of the base is 72 m. The surface area is 864 m squared.askedJun 8, 2013in ALGEBRA 2by johnkellyApprenticepyramid-surfacearea discover the surface ar area that a right consistent hexagonal pyramid with 2cm sides and 7cm slant heightaskedDec 9, 2013in GEOMETRYby chrisgirlApprenticesurface-area-of-a-hexagonal-pyramid a square based pyramidaskedAug 6, 2013in GEOMETRYby futaiScholarpyramid-surfacearea find the surface ar area that a square pyramid with a slant height of 15 and also a basic side measure of 20askedMar 4, 2014in GEOMETRYby rockstarApprenticesurface-area-of-a-square-pyramid the surface ar area that a hexigonal pyramid with a slant hight of around 17 and also edge the 8askedDec 9, 2013in GEOMETRYby futaiScholarsurface-area-of-a-hexagonal-pyramid uncover the surface ar area that a reg. Triangle pyramidaskedApr 26, 2014in GEOMETRYby anonymoussurface-area-of-a-triangular-pyramid discover the surface ar area that the pyramid.askedSep 9, 2018in ALGEBRA 2by abstain12Apprenticesurface-areapyramid A ideal triangle has actually one leg double as lengthy as the other with an area that 289 centimeter squared.askedAug 19, 2014in ALGEBRA 2by anonymousarea uncover the area surface ar of a prism v dimensions the 8in, 15 in, 17in and 9in (height)askedMay 16, 2017in GEOMETRYby anonymousareasurface-area-of-a-prism find the total surface area of a rectangular solid v a lenght that 9 ft a width of 11 ft and a elevation of 14 ft.askedMar 18, 2014in GEOMETRYby futaiScholarsurface-area-of-a-rectangular find the surface ar area the a ball with 30 cm. RadiusaskedMar 4, 2014in GEOMETRYby johnkellyApprenticesurface-arearadius discover the size of the radius the a round with a surface area ofaskedJul 17, 2013in PRECALCULUSby futaiScholarvolume-surface-area A crate of mass 5.0kg is moving on a smooth ice surface with a velocity that 6.0m/s (right).?askedNov 1, 2014in PHYSICSby anonymousforce have the formula for surface Area of best Circular Cone.askedAug 17, 2015in PRECALCULUSby anonymoussurface-arearight-circular-conevolume What is the lateral area and also the surface area that the ideal prism?askedJul 27, 2013in GEOMETRYby harvy0496Apprenticelateral-surface-area What is the surface space of a best circular cone if the cone"s diameter is 10cm and the lenght is 20cm.askedMar 18, 2014in ALGEBRA 2by chrisgirlApprenticesurface-area-of-a-conediameter-of-a-cone uncover the surface area and volume of a cubeaskedJun 8, 2013in ALGEBRA 2by anonymousApprenticesurface-areavolume whats the surface area that a cube v side length of 16 mm, and also whats the volume that the model?askedFeb 7, 2015in PRECALCULUSby anonymoussurface-areavolumes what is the surface area of a cylinder with a basic diameter of 4ftaskedJul 29, 2014in ALGEBRA 1by anonymoussurface-area-of-a-cylinder what is the surface ar area of a prism through the numbers 6,5,2askedMar 4, 2014in GEOMETRYby harvy0496Apprenticesurface-area-of-a-prism