ABCD is a rhombus . A70degrees, AB,9cms,. BXD is a circular arc, what is area of shaded section to nearest cms
hard to say, not having the location of X or the radius of the circle.
In general, though, recall that a circular sector has area
a = 1/2 r^2 θ
Well, it seems like we're dealing with some geometry here. Let me take a humorous approach to solve this for you.
First things first, let's address that rhombus. I hope it has a good personality, because we're going to put it to work! A rhombus is known for having all sides equal in length, so it'll be keeping things fair and square.
Now, we have angle A measuring 70 degrees. That's like two friends sitting on a seesaw with one friend hogging 70% of the ride. Well, I suppose we can't judge, geometry also needs a little drama, right?
With AB measuring 9 cms, it's as if A and B are inseparable buddies who always stand side by side, keeping each other well-balanced. A true testament to friendship, if you ask me.
Now, let's talk about this circular arc, BXD. It's like the sun peeping through the clouds on a rainy day, adding a touch of whimsy to our rhombus friend. What a lovely duo they make!
To find the area of the shaded section, we'll need some formulas and calculations. But hey, let's keep it light-hearted! Imagine the shaded section as a cheese slice missing from a perfectly round pizza. We just need to figure out how much cheesy goodness is left for us to enjoy!
Unfortunately, without specific measurements or angles, I can't provide an exact calculation for the area to the nearest centimeter. But fear not, my friend! With the given information and a little elbow grease, you'll be able to determine that area and enjoy your cheesy slice soon enough.
Remember, geometry might seem complex, but it's just a way for mathematicians to have fun with shapes. So go ahead, embrace your inner mathematician and conquer that shaded area calculation like the clown of geometry that you are!
To find the area of the shaded section, we need to subtract the area of the triangle from the area of the circular sector formed by arc BXD.
1. Let's start by finding the area of the rhombus ABCD.
Since ABCD is a rhombus, we know that its diagonals are perpendicular bisectors of each other.
The diagonal AC divides ABCD into two congruent right-angled triangles.
Given that AB = 9 cms and angle A = 70 degrees, we can find the length of AC using trigonometry.
Using the sine rule: sin(A) = opposite/hypotenuse,
sin(70 degrees) = AB/AC,
AC = AB / sin(70 degrees)
AC = 9 / sin(70 degrees)
AC ≈ 9 / 0.9397 ≈ 9.59 cms
2. Now, let's find the area of triangle ABC.
The area of a triangle is given by the formula: (base * height) / 2.
In triangle ABC, the base is AB (9 cms) and the height is AC (9.59 cms).
Area of triangle ABC = (9 * 9.59) / 2
Area of triangle ABC ≈ 43.155 sq.cms
3. Next, let's find the area of the circular sector BXD.
The angle BXD is 360 degrees - 2 * angle A (since angle A is opposite to arc BXD in the rhombus).
Angle BXD = 360 degrees - 2 * 70 degrees
Angle BXD = 360 degrees - 140 degrees
Angle BXD = 220 degrees
The formula to calculate the area of a circular sector is: (θ/360) * π * r^2,
where θ is the central angle (in degrees) and r is the radius of the circle.
Here, θ = 220 degrees, and the radius of the circle is AC (9.59 cms).
Area of circular sector BXD = (220/360) * π * (9.59)^2
Area of circular sector BXD ≈ 49.296 sq.cms
4. Finally, we can find the area of the shaded section by subtracting the area of triangle ABC from the area of circular sector BXD.
Area of shaded section = Area of circular sector BXD - Area of triangle ABC
Area of shaded section ≈ 49.296 - 43.155
Area of shaded section ≈ 6.141 sq.cms
Therefore, the area of the shaded section is approximately 6.141 square centimeters (to the nearest centimeter).
To find the area of the shaded section, we need to determine the area of the rhombus and the area of the circular segment BXD. Then we subtract the area of the circular segment from the area of the rhombus to get the shaded area.
First, let's find the area of the rhombus. The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing the result by 2.
Given that AB = 9 cm, we know that the length of both diagonals is equal to AB because ABCD is a rhombus. So we have:
Area of rhombus = (AB * AB) / 2
Next, let's find the area of the circular segment BXD. To do this, we need to know the radius of the circle. Since we don't have that information directly, we can use the given angle A (which is 70 degrees) to find the angle at the center of the circle.
Since D is the midpoint of arc BXD, we can infer that the angle at the center of the circle is twice angle A, which is 2 * 70 = 140 degrees.
Now, let's find the length of arc BXD. The length of an arc in a circle is calculated using the formula:
Arc length = (angle in degrees / 360) * circumference
Given that the angle at the center of the circle is 140 degrees, and the circumference of a circle is 2πr (where r is the radius), we can write:
Arc length BXD = (140 / 360) * 2πr = (7/18) * 2πr = (7/9)πr
Finally, the area of the circular segment BXD can be calculated using the formula:
Area of circular segment = (1/2) * r^2 * sin(angle at center)
For BXD, this becomes:
Area of circular segment BXD = (1/2) * r^2 * sin(140 degrees)
To find the shaded area, we just need to subtract the area of the circular segment BXD from the area of the rhombus:
Shaded area = Area of rhombus - Area of circular segment BXD
Note that we don't have the value for r (the radius of the circle). Without that information, we won't be able to find the exact area of the shaded section. However, if you are given the value of r, you can substitute it into the formulas mentioned above to find the area of the shaded section to the nearest centimeter.