Is the area and length of one of the diagonal of a rhombus are 24cm square and 8 cm respectively Then what will be the perimeter in Centimetre?

Question 11 Quadrilaterals Exercise 10B

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Answer:

We know that ABCD is a rhombus

It is given that AC = 24cm and BD = 18cm

In a rhombus we know that the diagonals bisect each other at right angles

Consider △ AOB

We know that

∠ AOB = 90

To find AO and BO

We know that

AO = ½ AC

By substituting AC

AO = ½ (24)

AO = 12 cm

BO = ½ BD

By substituting BD

BO = ½ (18)

BO = 9 cm

Based on the Pythagoras Theorem

AB2 = AO2 + OB2

By substituting values

AB2 = 122 + 92

So we get

AB2 = 144 + 81

By addition

AB2 = 225

AB = √ 225

So we get

AB = 15 cm

Therefore, the length of each side of the rhombus is 15 cm.

Video transcript

"hello students my name is rabbit singh and i welcome you all to lido learning homework one of india's best online classes now today in this video we have a question that is based on the topic rhombus the question says the length of the diagonals of a rhombus are 24 centimeter and 18 centimeters you can see we have made a figure that is abcd which is a rhombus and ac is one of the diagonals bd is the second diagonal the lengths are also given that we have written on the screen now let the diagonal of rhombus bisect each other at right angle so if they bisect each other at right angle so we have ao that means this oc equal 12 centimeter because if they are bisecting so this will become 12 and this will become 12. similarly bd is being bisected so that means ob is 9 and od is equal to 9. now let angle aod where this angle aod this angle aod that is equal to 90 degree now what you will do we have the two values that is 12 square 12 and 9 so we can apply the pythagoras theorem on this so pythagoras theorem means a b squared will be equal to what ao squared plus op squared now again in right angle triangle aod whereas aod aod this side we have 12 and 9 so applying the pythagoras theorem we will go get a d equals 15 centimeter 144 plus 81 so that will be equal to 225 so answer comes out to be 15 centimeter so we know in our rhombus all sides are equal so answer will be 15 centimeter so the question was uh what is the length of the rhombus of each side of the rhombus so if we have the side for one side if we have the lens for one side then all sides are equal so answer will be 15 centimeter i hope you have understood the concept very clearly but still if you have any doubt do comment in the comment box and please like and subscribe our channel for lido thank you "

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Rhombus area calculator is a great tool to determine the area of a rhombus, as well as its perimeter and other characteristics: diagonals, angles, side length, and height. Have a look on many ways you can find the diamond area: given diagonals of a rhombus, using base and height, side and any chosen angle... Are you still wondering how to find the area of rhombus or rhombus perimeter? Check the rhombus area formulas below or just experiment with the tool.

A rhombus is a simple quadrilateral with all sides equal. The other names are an equilateral quadrilateral or a diamond (like the one from playing cards ♢).

Fundamental properties of a rhombus are:

• The two diagonals of a rhombus are perpendicular and bisect each other,
• Its diagonals bisect opposite angles,
• Opposite angles have equal measure.

Every rhombus is a parallelogram and a kite.

There are three useful formulas for calculation of the area of the rhombus:

area = base * height

1. Knowing diagonals of a rhombus

area = (e * f)/2

1. Knowing side and any (!) angle

area = s² * sin(angle)

Why can we use any angle in the last rhombus area formula? Because we know that two adjacent angles are supplementary, and sin(angle) = sin(180° - angle).

There are other variations of those equations (as e.g. calculating the area given height and angle), but they are only simple trigonometric transformations of those three most popular rhombus area formulas.

Finding the rhombus perimeter is trivial if we know the side length - it's 4 * a. But what if we know only diagonals of a rhombus? Let's check:

1. We know that diagonals are perpendicular and bisect each other. So the rhombus is nothing else than four congruent triangles, with legs equal to e/2 and f/2.
2. All we need to do is finding the hypotenuse of the triangle. You can use here the right triangle calculator or Pythagorean theorem calculator.
3. Multiply by 4 the obtained hypotenuse value. It's your rhombus perimeter!

Also, you can use this formula:

• perimeter = 4 * √(e/2)²-(f/2)²)

Or just type the lengths of the diagonals into the rhombus area calculator!

Are you still pretty unsure how to use the calculator? Let's show its potential on the simple example:

1. Type the first given value you have. Let's assume it's side = 10 in.
2. Type the second given value. For example, an angle equal to 30°.
3. Wow! The rhombus area calculator is displaying all the other values - area, height, perimeter, angle and diagonals. Impressive, isn't it?

Our tool is really flexible - if it's possible to calculate, it will do it. Usually two given values are enough, give it a try!

The answer is yes to both questions. Every square is a rhombus, as for a rhombus the only necessary condition is that it needs to have all sides of equal length. As you know perfectly well, a square needs to have all sides equal and all four equal angles, so it fulfills the conditions to be a rhombus.

Similarly, a rhombus is a parallelogram, as any shape needs to have two pairs of parallel sides to be a parallelogram - and the rhombus has them. So the rhombus is always a parallelogram, but parallelogram is a rhombus only in a special case - for a parallelogram with four sides of equal length.