(1)
Best formula to use is as follows -
V = h/3(Areatop + √(Areatop*Areabottom) + Areabottom)
(2)
To find (h) using a tape measure -
Areatop => bd
Areabase => ac
Lateral edge remaining => e (from top corner to base corner)
k = 1 - √(bd/ac)
H= √([e/k]² - [a/2]² - [c/2]²)
h = Hk
V = H/3*(ac-bd+bd*k)
(3)
Lets say Top is a rectangle with sides b & d
and bottom is a rectangle with sides a & c respectively.
Let height be h
in that case the volume of Truncated Pyramid with rectangular base will be -
V = 1/3((a²c-b²d)/(a-b))h
BUT BE CAREFUL - a,b,c,d are not all independent variables (one depends on the others) so this answer is misleading!!!
Proof -
Suppose the height of Full Pyramid is H
From parallel line property
(H-h)/H = b/a
Rearranging
H = ah/(a-b) --------------------(1)
Also
Since V=1/3 Base area X Height
Volume of full pyramid = 1/3 X ac X H
Volume of removed Pyramid = 1/3 X bd X (H-h)
So volume of truncated part V = 1/3(acH-bd(H-h))
=1/3((ac-bd)H + bdh)
From (1)
V = 1/3((ac-bd)ah/(a-b) + bdh)
reducing and rearranging we get
V = 1/3((a²c-b²d)/(a-b))h
(4)
In case the truncated solid forms a prism instead, we have following formula -
V = ( h/6)(ad + bc + 2ac + 2bd)
Proof -
Fig(1)
Fig(2)
Lets divide the fig(1) into four different shapes as shown in fig(2)
VA = Volume of cuboid = bdh
VB = Volume of prism after joining both Bs= ½ X base X height X width = ½ (a-b) (d)(h)
VC = Volume of prism after joining both Cs = ½ X base X height X width = ½ (c-d) (b)(h)
VD = Volume of rectangular pyramid after joining all Ds = 1/3 X base area X height =
1/3 (a-b) (c-d) h
Then V = VA + VB + VC + VD
Or, V = bdh + 1/2(a-b)dh +1/2(c-d)bh + 1/3(a-b)(c-d)h
Arranging and simplifying we get -
V = ( h/6)(ad + bc + 2ac + 2bd)
a estimate is based on known information it is just not a true answer.
IQ is not based on age, it's based on intelligence.
Qualitative is the grouping of things based on their qualities. Quantitative is based off of the quantity, or amount there is, of something.
The probability based on an event that has already occurred is 100%. If the event has occurred, it has occurred.
No. Outliers are part of the data and do not affect them. They will, however, affect statistics based on the data and inferences based on the data.
The volume of any pyramid or cone is given by the formula: 1/3 x base area x height For a rectangular-based pyramid: 1/3 x base width x base length x height
I don't really understand your question, but one example of a rectangular based pyramid is the Great Pyramid in Giza.
It is a frustum of a rectangular pyramid.
In trigonometry, we call it a rectangular pyramid.
A rectangle based pyramid!
A heptahedron.There are 34 distinct heptahedra: some of these are:a hexagon based pyramid,a pentagon based pyramid with one of the basal vertices truncated,a cuboid with one of its vertices truncated.
a rectangular based pyramid
A rectangular prism has 8 vertices whereas rectangular based pyramid has 5 vertices
A rectangular based pyramid has 5 vertices, 8 edges and 5 faces
five A triangular based prism has 5 A triangular based pyramid has 4 and there is no such thing as a triangular based prism pyramid - unless you mean a truncated pyramid (or a frustum) which is essentially a prism.
a rectangular based pyramid has got 6 edges and four faces and four vertices.
You start with a quadrilateral based bipyramid, which has six vertices. At each vertex, remove the tip in the form of a quadrilateral based pyramid. You will be left with a truncated octahedron.