Building Space – When talking about geometric shapes, the thing that comes to Sinaumed’s’ mind is the cube and square shapes which are also part of the Mathematics subject matter. Yep, these spatial shapes have been introduced to us since childhood , you know , especially when we were still in grade 2 elementary school. That’s why, we often don’t feel foreign and find it easy to guess what types of spatial shapes are around us, because the brain has already processed them. in quite a long time. This material was not immediately finished, because when I was in junior high school (SMP) I also studied it. Even now, exam questions for CPNS also use this geometric material, of course at the C3 question levelyes…
Then, build that space what is it? What are the other types of geometric shapes other than cubes and squares? What are the properties and formulas for calculating the types of geometric shapes? So, so that Sinaumed’s doesn’t feel confused for a long time, let’s look at the following review!
What is Build Space?
Since the geometry material is included in Mathematics, specifically in the Geometry chapter, then of course there will be formulas and their completion processes. Just a little trivia , the reason why the Geometry chapter is taught from an early age is because some of the indicators can be found in everyday life, as well as real examples of objects.
Geometry which is part of Mathematics as a whole discusses how the shape and size of an object with a certain regularity. When introduced to students at the elementary school education level, it is only limited to knowing how a ball and what is not a ball are; what is the shape of a triangle and what is not a triangle; what is the shape of the tube and what is not the tube; and others. Then, in the following classes, the material will be further developed by starting to draw spatial shapes to calculating volume using formulas.
Basically, this geometric shape is a 3-dimensional shape that has volume. According to Sri Subarinah (2006), a spatial shape is a 3-dimensional geometric shape with boundaries in the form of flat planes and curved planes. Meanwhile, according to Sumanto et al (2008), argues that a spatial shape must have certain characteristics, starting from the presence of sides, edges, and vertices.
It should be noted that these sides, edges, and vertices are generally only owned by geometric shapes with 3 dimensions, right? The sides (planes) are part of the geometric shape that separates the inside and outside. Then, the edge is the meeting line between the two sides of the geometric shape. Furthermore, there is a corner point which is usually at the end or corner of this geometric shape which is the meeting point between the three ribs. So, based on these definitions, it can be concluded that,
“A spatial shape is a three-dimensional geometric shape that has certain properties, namely the presence of sides (planes), ribs, and vertices.”
Of course, this spatial structure has various types, not just cubes and blocks. The division of the types of geometric shapes is based on the shape of the plane, whether flat or curved. But usually, learning these types of geometric shapes does not apply to flat planes and curved planes, so students are only asked to “memorize” them. When in fact, it would be easier if you divide it on the shape of the field.
In a flat plane shape, there are 4 types of shapes, starting from cubes, blocks, prisms, and pyramids. Meanwhile, in curved plane shapes there are 3 types of shapes namely cylinders, cones, and spheres. Examples of these types of geometric shapes can be easily found around us. For example, the shape of the cube is dice and Rubik’s toy. Then, an example of a block shape is a jenga toy cardboard box. Meanwhile, an example of a cone shape is a birthday hat and an ice cream cone .
Building Space Parts
1. Side (Field)
The alias side of this field becomes a field in the geometric shape that separates the inside from the outside. This side has 2 forms, namely the flat side and the curved side.
2. Ribs
Namely a line segment formed by the intersection of two facets that meet. Ribs can be straight lines or curved lines. Ribs that lie on one side of the plane and do not intersect each other are called parallel edges. Then, ribs that intersect but are not on one side of the plane are called crossed edges.
3. Corner Point
Namely the meeting point between three or more ribs in a geometric shape.
4. Diagonal Side
Namely a line segment that connects two vertices that lie on different edges on one side of the plane.
5. Diagonal Space
Namely the area of the line that connects two corner points, each of which is located on the top side and the base side.
6. Diagonal Field
Namely the field that is bounded by the presence of 2 pieces of diagonal side and opposite. Usually found in cubical and rectangular shapes.
7 Types of Building Spaces and Their Formulas and Properties
Build a Flat Side Room
1. Cube
Properties of the Cube
- Has 6 sides: abcd, adeh, bcfg, cdgh, and efgh.
- Has 12 ribs.
Base ribs: ab, bc, cd, and ad.
Top rib: ef, fg, gh, and eh.
Straight ribs: ae, bf, cg, and dh.
- Has 8 vertices: a with g; b with h; c with e; d with f.
- It has 12 diagonal sides: ac and bd; eg and fh; af and b; ch and dg; bg and cf; ah and de.
- There are 4 space diagonals: ag and ce; bh and df.
- There are 6 diagonals: abgh, acge, adgf, bche, bdhf, and cdef.
- The sides of the plane must be square with the same size.
Examples of Cube Nets
The cube shape has more than four grid patterns. Well, here is an example of a grid pattern on a cube!
Formulas and Example Questions
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- It is known that a cube has a side of 10 cm. What is the total volume of the cube?
Answer:
Given: side = 10 cm
Wanted: volume of a cube
Solution : Sз = 10 x 10 x 10 = 1,000 cmз
So, the volume of the cube is 1000 cmз
2. Blocks
Beam Properties
- Has 6 sides: ABCD, EFGH, BCFG, ADEH, ABEF, CDGH.
- Has 12 ribs: (AB, EF, CD, GH) (BC, AD, EH, FG) (AE, BF, CG, DH)
- It has 8 vertices: A, B, C, D, E, F, G, and H.
- Has 12 diagonal faces: (AC, BD, EG, FH) (AF, BE, DG, CH) (AH, DE, BG, CF), which is AC ≠ AF ≠ AH
- There are 4 space diagonals: AG, BH, CE, DF
- There are 6 diagonal planes: ACGE and BDHF, AFGD and BEHC, BGHA and DFED.
- The sides of the plane are rectangular.
Examples of Beam Nets
The block room shape has more than four grid patterns. Well, here’s an example of a net shape pattern on a beam!
Formulas and Example Questions
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- A cuboid has a length of 7 cm, a width of 4 cm and a height of 5 cm. Calculate the volume of the block!
Answer:
Given: length = 7 cm, width = 4 cm, height = 5 cm
Wanted: the volume of the block
Completion
Block volume = (pxlxt)
= ( 7 x 4 x 5) = 140 cm3
So, the volume of the block is 140 cm3.
3. Prism
Basically, this prism becomes a geometric shape bounded by two parallel planes (the base plane and the top plane), while the other planes intersect according to the parallel edges. These other planes are called vertical planes. Then, the distance between the two planes (the base plane and the top plane) is called the height of the prism. According to Sa’dijah (1998), this prism is a polyhedron with two sides facing each other.
Prism Types
If seen from how the shape of the base field, the prism can be divided into 3 types, viz.
- A triangular prism, which is a triangular prism.
- Quadrilateral prisms and so on, ie those whose base is rectangular or so on (pentagon, hexagon, etc.)
- Parallelepipedal prism, namely the base plane in the form of a parallelogram.
Examples of Prism Nets
Since there are many types of prisms depending on the shape of the base, the following examples of nets are triangular prisms.
Prism properties
- It has a base plane and a top plane that are parallel in shape and congruent.
- It has a parallelogram-shaped side plane.
- All the ribs are parallel and the same length.
- All the diagonals are parallelograms.
- In an n-sided prism, the number of diagonal fields is n/2 (n-3)
- In an n-sided prism, the number of space diagonals is n(n-3)
Formulas and Example Questions
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- There is a pentagonal prism with a base area of 50 cm and a height of 15 cm. What is the volume of the prism?
Answer:
Given: area of base = 50 cm, height = 15 cm
Wanted: prism volume
Completion
Prism volume = base area x height
= 50 cm x 15 cm = 750 cm
So, the volume of the pentagonal prism is 750 cm.
4. Limas
A pyramid is a geometric shape that is bounded by the existence of a (n) side and several triangles with common vertices outside the plane of the (n) side. Well, consider the following example of a pyramid image! The red lines in the middle (t) are called the height of the pyramid, while the T point above is called the peak point.
Almost the same as a prism, this pyramid also has several types based on the shape of its base. Especially in triangular pyramids, because the upright sides are triangular, the pyramid does not have an upper side, but has a vertex. The main elements that are owned by pyramids are the corner points, edges, and contents.
Types of Limas
- Arbitrary pyramid, namely a pyramid whose base is in the form of an arbitrary n-sided shape and the vertex is also arbitrary.
- Regular pyramid, which is a type of pyramid whose base is in the form of a regular n-sided shape. The projection at the apex coincides with the center of the base plane.
Properties of Regular Plumes
- In a regular n-sided pyramid, the base will be a regular n-sided. Then, all the uprights are the same length, with all the perpendiculars congruent, and all the apothemes are the same length. It should be noted that the apothem is the distance between the apex and the base.
- Has a pyramid height which is the distance from the apex to the projection which is located at the base of the pyramid.
- It has the apex of the pyramid, with the meeting point of the vertical side planes in the shape of a triangle.
Consider the example of a rectangular pyramid and the following description of its properties!
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Examples of Limas Nets
Sinaumed’s must have understood that there are several types of pyramids depending on the shape of the base. That is why the nets can also be different from one another. Well, here is an example of a rectangular pyramid net.
Limas Formula
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Build a Curved Side Room
1. Tube
Examples of cylindrical objects around us are drink cans and pipes. Soenarjo (2008), argues that this cylindrical shape has the same circle at the top and bottom. Then, according to Soewito, et al (1992) also stated that this tube has a simple closed surface whose boundaries are also part of the tube itself and the base is a circle. Yep, a cylindrical shape is seen as a special prism with a circular base.
Tube properties
- It has 3 sides, namely the top side, the base side, and the tube blanket.
- It has no vertices because its shape is a circle.
- The top and bottom planes, which are circular in shape, must have the same size.
- There is a curved side called a tube blanket.
- There is a tube height which is the distance between the top plane and the base plane.
- Has 2 curved ribs.
Tube Nets
If Sinaumed’s looks at the following figure, it will be clear that the tube net is composed of a rectangle and two circles.
The formula for calculating tubes
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2. Cones
Examples of objects in the shape of a cone shape are birthday hats, ice cream cones, oil cones, and many others. Sumanto, et al (2008) stated that this cone is bounded by a circular base and a curved side. This curved side is in the form of a blanket that is conical towards the top, the higher it is, the smaller or sharper it is.
Cone Properties
- Circular pedestal.
- It has 2 sides, namely the circle below and the curved plane (cone blanket).
- There is a conical blanket in the form of a curved side.
- Has 1 curved rib.
- Has a high point.
- There is a cone height which is the distance from the apex to the base.
Cone Nets
If you pay attention, these conical nets look like pizza slices and are small round shapes …
Cone Calculating Formulas
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3. Ball
The existence of this curved side shape must have often been encountered by Sinaumed’s around the neighborhood, even with the same name. Yep, this spherical shape also includes three-dimensional shapes that are part of Geometry.
Ball Properties
- It only has 1 side, which is a collection of points equidistant from the center of the ball. This side of the ball is also called a ball blanket.
- Has no ribs.
- Has a ball radius that connects the center point of the ball to the surface point. The radius of this ball is written as an “r”.
- The diameter is twice the radius of the ball.
- Has a spherical chord in the form of a line space that connects 2 points on the ball.
Ball Counting Formula
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