A right pyramid has its apex aligned right above the center of the base.
Right Pyramid
Definition
A right pyramid is a pyramid whose apex is aligned exactly above the center of the base. Thus, a perpendicular line joining the apex and the base center is the height of a right pyramid.
Unlike a right pyramid, an oblique pyramid does not have its apex aligned away from the center of the base.
Some common right pyramids with different bases are:
Right Triangular Pyramid
It has a triangular base with its apex aligned directly above its center.
Right Triangular Pyramid
Right Square Pyramid
It has a square base with its apex aligned directly above its center.
Right Square Pyramid
Right Rectangular Pyramid
It has a rectangular base with its apex aligned directly above its center.
Right Rectangular Pyramid
Right Pentagonal Pyramid
It has a pentagonal base with its apex aligned directly above its center.
Right Pentagonal Pyramid
Right Hexagonal Pyramid
It has a hexagonal base with its apex aligned directly above its center.
Right Hexagonal Pyramid
Like all other polyhedrons, we can calculate the surface area and volume of a right pyramid.
Formulas
Surface Area
The formulas is:
Surface Area (SA) = ${B+\dfrac{1}{2}Ps}$, here B = base area, P = base perimeter, s = slant height,
Also ${\dfrac{1}{2}Ps}$ = lateral surface area (LSA)
∴ SA = B + LSA
Let us solve some examples to understand the above concept better.
Find the lateral and the total surface area of a right pyramid with a base perimeter of 36 cm, base area of 81 cm2, and slant height of 16 cm.
Solution:
As we know, Lateral Surface Area (LSA) = ${\dfrac{1}{2}Ps}$, here P = 36 cm, s = 16 cm ∴ LSA = ${\dfrac{1}{2}\times 36\times 16}$ = 288 cm2 Total Surface Area (TSA) = B + LSA, here B = 81 cm2, LSA = 288 cm2 ∴ TSA = 81 + 288 = 369 cm2
Find thesurface area of a right pyramid with a square base of 6 cm, and a slant height of 9.5 cm.
Solution:
Here we will use the specific surface area formula for a right square pyramid. Total Surface Area (TSA) = b2 + 2bs, here b = 6 cm, s = 9.5 cm ∴ TSA = 62 + 2 × 6 × 9.5 = 150 cm2
Volume
It is the space it occupies in a 3-dimensional plane. It is expressed in cubic units such as m3, cm3, mm3, and in3.
The general formula is given below:
Volume (V) = ${\dfrac{1}{3}Bh}$, here B = base area, h = height
Let us solve an example to understand the above concept better.
Find the volume of a right pyramid with a base area of 160 cm2 and a height of 16 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{3}Bh}$, here B = 160 cm2, h= 16 cm ∴ V = ${\dfrac{1}{3}\times 160\times 16}$ = 853.33 cm3
Find the volume of a right triangular pyramid with a basearea of 2.3 cm2 and a height of 5 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{3}Bh}$,here B = 2.3 cm2, h = 5 cm ∴ V = ${\dfrac{1}{3}\times 2.3\times 5}$ = 3.83 cm3
Find the volume of a right square pyramid with a base of 6 cm and a height of 8 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{3}b^{2}h}$, here b = 6 cm, h = 8 cm ∴ V = ${\dfrac{1}{3}\times 6^{2}\times 8}$ = 96 cm3
Find the volume of a right rectangular pyramid with a base length of 10 cm, a base width of 6 cm, and a height of 12 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{3}lwh}$, here l = 10 cm, w = 6 cm, h = 12 cm ∴ V = ${\dfrac{1}{3}\times 10\times 6\times 12}$ = 240 cm3
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