Rhombus ABCD is similar to rhombus BFDE.The area of rhombus ABCD is 24 and angle BAD=60 degrees .What is the area of rhombus BFDE?
Hi Reddy,
The answer for this question is 8.
the answer is 8
To find the area of rhombus BFDE, we can use the fact that the area of a rhombus is half the product of its diagonals. However, since we do not have the length of the diagonals of rhombus ABCD, we will need to find them first.
Let's start by analyzing the given information. We know that the area of rhombus ABCD is 24, which means:
Area(ABCD) = 24
Since the area of a rhombus is half the product of its diagonals, we can write the formula as:
Area(ABCD) = (d1 * d2) / 2
where d1 and d2 are the diagonals of the rhombus ABCD.
Now let's work on finding the length of the diagonals. Since rhombus ABCD is similar to rhombus BFDE, their corresponding angles are equal. We are given that angle BAD is 60 degrees. In a rhombus, opposite angles are equal, so we can conclude that angle BFD is also 60 degrees.
Now, let's consider triangles BAD and BFD. These triangles are similar because they have two angles that are equal (60 degrees) and one pair of corresponding sides (BF and BA).
Using the Law of Sines, we can establish a proportion between the side lengths of the two triangles:
(BF / sin(BFD)) = (BA / sin(BAD))
Substituting the known values:
(BF / sin(60)) = (BA / sin(60))
Since sin(60) = √3 / 2, the equation simplifies to:
(BF / (√3 / 2)) = (BA / (√3 / 2))
Multiplying both sides by (√3 / 2), we get:
BF = BA
This means that the length of side BF is equal to the length of side BA.
Since rhombus ABCD is similar to rhombus BFDE, their corresponding sides are proportional. Hence, we can conclude that the length of the diagonals of BFDE is also equal to the length of the diagonals of ABCD.
Now we can use the formula for the area of a rhombus to find the area of BFDE:
Area(BFDE) = (d1 * d2) / 2
Since the length of the diagonals of BFDE is equal to the length of the diagonals of ABCD, we have:
Area(BFDE) = (d1 * d2) / 2 = 24
Therefore, the area of rhombus BFDE is also equal to 24.
I noticed, looking at the "Related Questions" below, that you have posted this same question 3 times
The reason you are not getting any answers is that you don't have enough information.
We know nothing about the second rhombus.
BTW, the area of similar shapes is proportional to the square of their corresponding sides
you can find the side of the first:
Draw the diagonal BD, cutting the area in half
so triangle ABD = 12
area = (1/2)(a)(b)sinØ , where a and b are two sides with Ø the contained angle.
(1/2)(x)(x)sin60 = 12
x^2 (√3/2) = 24
x^2 = 48/√3
x = √ (48/√3 ) = 4√3/(√(√3) ) = appr 5.264