The area of a rhombus – When talking about a flat shape, it seems that almost everyone already knows it. This is because the flat shape lesson itself has been taught since someone was still studying in elementary school (SD). That’s right, during elementary school, it wasn’t just flat shapes, but we also learned about spatial shapes.
Whether it’s a flat shape or a flat shape, both of them can be used in everyday life. In this case, what is meant by what can be used is the formula of the plane shape and its spatial shape. In our life, of course we cannot be separated from flat shapes, such as cupboards, refrigerators, doors, balls, to diamonds which are one of the special foods when Eid al-Fitr and Eid al-Adha arrive.
For some people, they may only know square, rectangular, and triangular shapes. However, actually there are many other examples of flat shapes, such as trapezoids, parallelograms, rhombuses, and others. Each formula for a flat shape is certainly different, so when talking about flat shapes we should already know the formulas, namely the area formula and the circumference formula.
In fact, it would be even better if we also know a few questions from the formula for the area and perimeter of a geometric figure. That way, it will be easier to calculate the area and perimeter of a geometric shape. For some people, they may have forgotten how to formula and perimeter, so they need to open the internet or books when they are still in school.
If we talk about all the shapes and shapes in one article, it will be very difficult or you could say it will be very long. Therefore, this time, we will first discuss about geometric shapes.
Even so, we will not discuss all flat shapes, You, but we will only discuss rhombus shapes. Not only the definition of a flat shape, but we will learn together about the formula for the circumference and the formula for the area of a rhombus. In fact, this article will also provide examples of questions on the area and perimeter of a rhombus.
So, what are you waiting for, without further ado, we will discuss more about the flat shape of a rhombus, starting from understanding, circumference, to area. So, read this article to the end, You.
Definition of Rhombus
A rhombus is a flat shape that has four sides that are the same length with the opposite sides parallel to each other and not perpendicular to each other. The four sides of a rhombus are the same length because a rhombus is formed from two congruent isosceles triangles. The following are the kinds of rhombus formulas for plane shapes and spaces in mathematics.
Rhombus Circumference Formula
The perimeter of a rhombus is the sum of all the side lengths or four times the sum of the side lengths. So, the formula for the circumference of a rhombus is K = 4s with K as the symbol for the circumference. While s is the side length.
Problems example:
Problem 1
Given a rhombus ABCD with AB = (4x-8) cm and BC = (96-4x) cm. Find the value of x and the perimeter of the rhombus.
Discussion: The sides of a rhombus are the same length, then: AB = BC
4x-8 = 96-4x
8x = 104
x = 13
After knowing the value of x, substitute that value into one of the equations.
AB = 4x – 8
AB = 4(13) – 8
AB = 44 cm
So, it is known that the length of side AB is 44 cm. Plug that number into the formula for the circumference of a rhombus.
K = 4s
K = 4(44)
K = 176 cm
So, the perimeter of the rhombus is 176 cm.
Problem 2
A rhombus has a side length of 13 cm. What’s the circumference?
Discussion:
K = 4s
K = 4(13)
K = 52 cm
Or it can be described as follows. Perimeter = Sum of the four sides, then:
K = side + side + side + side
K = 13 + 13 + 13 + 13
K = 52 cm
So, the perimeter of a rhombus is 52 cm.
The Area of a Rhombus Formula
The area of a rhombus is half the length of its diagonals. Then the formula for the area of a rhombus is ½ × d1 × d2. For information, d1 and d2 are the diagonals of a flat rhombus.
Problems example:
Problem 1
Look at the picture below
Problem 2
If a rhombus is known as PQRS with length PR = 6 cm and QS = 10 cm. So, what is the area of the rhombus?
Discussion:
Given: PR = d1 = 6 cm; QS = d2 = 10 cm. L = ½ × d1 × d2 L = ½ × 6 × 10 L = 30 cm2 So, the area of the rhombus is 30 cm2.
A rhombus ABCD has diagonals AC = 12 cm and BD = 16 cm. Calculate the area of the rhombus! Discussion: Given: AC = 12 cm; BD = 16 cm L = ½ × d1 × d2 L = ½ × 12 × 16 L = 96 cm2 Then, the area of the rhombus is 96 cm2.
Rhombus Elements
1. Four Equal Sides
It has four sides that are the same length and a pair of sides that are parallel to each other. In the figure, side AB = BC = CD = AD. While the sides AB // CD and AD // BC.
2. Two Unequal Diagonals
It has two diagonals that are unequal in length, the two diagonals are perpendicular to each other. Then AC ≠ BD.
3. Opposing Angles Are Equal
Opposite angles in a rhombus are equal and are bisected by the diagonal, so angles ∠A = ∠C and ∠B = ∠D.
4. Adjacent Angles are Straight
Adjacent angles are complementary. Then ∠A + ∠B = 180° and ∠C and ∠D = 180°. A rhombus has two axes of symmetry, namely its diagonal lines (AC and BD).
5. There is an isosceles triangle
Triangles ABD and CBD are isosceles triangles, so the angles ∠ADB = ∠ABD and ∠BDC = ∠DBC.
Rhombus Prism
A rhombus prism is a geometric shape that has a rhombus-shaped base and roof. Then, the rhombus prism covers are rectangular in shape. The elements of a rhombus prism, among others:
- Sides: The planes that form and delimit geometric figures. There are 6 sides in a rhombus prism.
- Edge: A line segment that is the intersection of two sides of a geometric shape. There are 12 edges in a rhombus prism.
- Corner point: Where three ribs meet. A rhombus prism has 8 vertices.
- Diagonal side: A line segment connecting two opposite angles on one side of a prism. There are 12 diagonals in a rhombus prism.
- Space diagonal: A line segment connecting two vertices of a prism that are not on one side or plane. There are 4 space diagonals in a rhombus prism.
- Diagonal plane: Plane made through the diagonals of the parallel sides of the base. A rhombus prism has 6 diagonals.
Rhombus Prism Volume Formula
The volume of a prism can be calculated by knowing the area of the base and the height. The formula for the volume of a rhombus prism is ½ × d1 × d2 × t. So, it takes the length of both diagonals as well as the height to calculate the volume of the rhombus prism. Volume units are written with the cube symbol, for example cm3 or m3.
Example problem:
A rhombus ABCD has a diagonal AC = 10 cm, BD = 12 cm, and a height of 3 cm. Calculate the volume of the prism!
Discussion:
Given: AC = 10; BD = 12; t = 3 cm
V = ½ × d1 × d2 × t
V = ½ × 10 × 12 × 3
V = 180 cm3
So, the volume of the rhombus prism is 180 cm3.
The formula for the surface area of a rhombus prism
The surface area of the prism is the sum of both the base and the cover (vertical sides). The formula for the surface area of a rhombus prism is 2 × base area + (base circumference × height) or L = 2 × (½ × d1 × d2) + (4s × t).
Information:
L = Surface area of the prism
d1 and d2 = Length of the
base diagonal s = Length of side
t = Height of the prism
Example problem:
A rhombus prism has base diagonals of 12 cm and 16 cm. The side length is 10 cm and the height is 5 cm. Calculate the surface area of the prism.
Discussion:
Given: d1 = 12 cm; d2 = 16cm; s=10cm; t = 5 cm
Use the formula for the surface area of a rhombus prism.
L = 2 × (½ × d1 × d2) + (4s × h)
L = 2 × (½ × 12 × 16) + (4(10) × 5)
L = 2 × (96) + (200)
L = 392 cm2
So, the surface area of the rhombus prism is 392 cm2.
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Closing
Basically, the rhombus flat shape has been taught since elementary school (SD). Even so, there is nothing wrong if we want to learn again about the various kinds of flat shapes. This is because the flat shape that we learned in the past can be used for the present.
Indeed, it will be difficult because you have to remember several formulas for the area and perimeter of a rhombus. However, after reading this article to the end, it is hoped that it will be easier for you to understand the flat rhombus shape. So, hopefully this article will be useful for You in the future.