A square pyramid identified by a square base is a three-dimensional shape having five faces, thus referred to as a pentahedron. The many famous example of together a square pyramid is the good Pyramid that Giza. A pyramid is a polyhedron that has actually a base and 3 or greater triangular faces that meet at a point over the base (the apex). Interestingly, pyramids are called after your base, together as
Rectangular pyramidTriangular pyramidSquare pyramidPentagonal pyramidHexagonal pyramid| 1. You are watching: How many faces does a square pyramid have | What is a Square Pyramid? |
| 2. | Properties of a Square Pyramid |
| 3. | Types the Square Pyramids |
| 4. | Square Pyramid Formula |
| 5. | Net that a Square Pyramid |
| 6. | FAQs top top Square Pyramid |
What is a Square Pyramid?
A square pyramid is a three-dimensional geometric shape that has actually a square base and four triangle bases that are joined at a vertex. The is a polyhedron (pentahedron) with five faces. A square pyramid is composed of a square base and four triangles connected to a vertex. Its base is a square and also the side faces are triangles with a usual vertex.
A square pyramid has three components.
The top point of the pyramid is called the apex.The bottom square is called the base.The triangular sides are referred to as faces.
Properties of a Square Pyramid
Let united state list out the nature we have actually explored in the above image. All these properties are derived from the an interpretation of a pyramid.
It has actually 5 faces.It has 4 side faces that room triangles.It has 5 vertices.It has actually 8 edges.Types the Square Pyramids
We can identify the square pyramids ~ above the basis of the lengths of your edges, position of the apex, and so on. Allow us talk about the different varieties of square pyramids.
Right square pyramid
If the apex the the square pyramid is right above the center of the base, it forms a perpendicular v the base. Such a square pyramid is dubbed the appropriate square pyramid.
Oblique square pyramid
If the apex that the square pyramid is not aligned right over the center of the base, the pyramid is dubbed an slope square pyramid.
Equilateral square pyramid
If every the triangular faces of a square pyramid have equal edges, climate the square pyramid is referred to as an it is provided square pyramid.
Square Pyramid Formula
There room formulas for square pyramids because that finding the volume, height, basic area, and surface area. Below you can see the formulas of the volume, complete surface area (TSA), and lateral surface area (LSA) of square pyramid.
Base Area of a Square Pyramid
Since the square pyramid has a square base, we can calculate its basic area making use of the exact same formula as the area the square, which is next × next or base edge2.
Example: Assume that the basic edge that a square pyramid is given as 7 units. Then, the basic area the the square pyramid is: BA = 7 × 7 = 49 square units
Volume the a Square Pyramid
The formula to identify the volume of a square pyramid is: V = <(1/3)a2h>. Here, a is the size of the base and also h is the perpendicular height.
Example: Assume the the elevation (h) and also the size of the basic edge (a) room 9 units and also 5 units, respectively. Then, the volume the the square pyramid is:
Volume = 1/3 x 52 x 9 = 1/3 x 25 x 9 = 75 cubic units
Surface Area of a Square Pyramid
There room two species of surface ar areas, one is TSA (Total surface ar Area), and the other is LSA (Lateral surface ar Area). When we talk around its surface ar area, we generally refer come its complete surface area (which is the sum of locations of every faces), vice versa, the lateral surface area is the sum of the locations of the side deals with only. Think about a square pyramid of base edge 'a', elevation 'h', and slant 'l'.
The formula to calculate the surface area that a square pyramid as soon as its elevation h and also base edge a are given: surface Area = a2 + 2a√<(a2/4) + h2>The formula to calculation the surface ar area the a square pyramid as soon as its slant elevation l and base leaf a room given: surface Area = a2 + 2alThe formula to calculation the curved surface area or lateral surface ar area the a square pyramid is given as: 2a√<(a2/4)+ h2> or 2alExample: Assume that the elevation h and also the length of the basic edge a space 9 units and also 5 units, respectively.
Then, the surface ar area the the square pyramid is:
Surface area = (5)2 + 2 x 5 √<(52/4) + 92>
= 25 + 10 √<(25/4) + 81>
= 25 + 10√(349/4)
= 25 +10 x 9.34
= 25 + 93.4
= 118.4 square units.
The net of a square pyramid offers a flattened watch of each face and the square base together with its dimensions. When placed horizontally, the network of the pyramid through a square base is viewed in a 2D shape and when urgent the solid form becomes a 3D form of a square pyramid. The net of a square pyramid has actually the same number of faces when it is flattened. The net of any type of solid shape helps in detect the surface ar area of that solid shape. The image listed below showcases the flattened see of a square pyramid with its faces and also base.
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Example 1: Identify the square pyramid.
Solution:
Pyramids are named as per their bases. Thus, the names of the forms are as follows.
The base of the an initial pyramid is a triangle. Thus, that is a triangle pyramid.The basic of the 2nd pyramid is a square. Thus, that is a square pyramid.The basic of the third pyramid is a pentagon. Thus, the is a pentagonal pyramid.The basic of the 4th pyramid is a hexagon. Thus, the is a hexagonal pyramid.Therefore, the second one is a square pyramid.
Example 2: Daniel is building a close up door square pyramid-shaped aquarium in his backyard. The basic edge the the square pyramid is 10 inches and also the slant height is 15 inches. Aid Daniel identify the complete surface area that the aquarium.
Solution:
Given, the slant elevation l the the square pyramid is 15 inches, the base edge a that the square pyramid is 10 inches.
Thus, The total surface area the the aquarium is given by: a2 + 2al
= 102 + 2 × 10 × 15
= 100 + 300 = 400 in2
Therefore, the Surface Area the the aquarium = 400 square inches.
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Example 3: Sophia has a vessel in the form of one inverted constant square pyramid that has to be filled v water. The altitude of the vessel is 10 inches and the basic edge is 7 inches. What is the volume the water Sophia can fill in the vessel?
Solution:
Given, the elevation h that the ship is 10 inches and the base edge the the ship is 7 inches.