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Find the area of a Rhombus whose side is 6cm and altitude is 4cm. If one of the diagonal is 8cm long find the length of the other diagonal?
Wiki User
∙ 14y ago
Rhombus Area = side x height = 6 cm x 4 cm = 24 cm2
In the right triangle formed by the side and the height of the rhombus, we have:
sin (angle opposite to the height) = height/side = 4 cm/6cm = 2/3, so that
the angle measure = sin-1 (2/3) ≈ 41.8⁰.
In the triangle formed by two adjacent sides and the required diagonal, which is opposite to the angle of 41.8⁰ of the rhombus, we have: (use the Law of Cosines)
diagonal length = √[62 + 62 -2(6)(6)cos 41.8⁰] ≈ 4.3
Thus, the length of the other diagonal of the rhombus is about 4.3 cm long.
Wiki User
∙ 14y ago
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What is the formula for a rhombus in math?
Area=ba where b=base (any side), and a=altitude, the perpendicular length from the base to the opposite sideORArea= (d1*d2)/2 where d1 is the diagonal and d2 is the other diagonal
How do you find the area of a rhombus?
Area = base x height.This formula also works for parallelograms, rectangles and squares.You find the area of a rhombus by multiplying l times h (length times height) where the height means the perpendicular distance from one side of length l to the other side.There are three ways to find the area of a rhombus, but these two ways are the easiest.You can use A = ba (base times altitude/height)You can use A= 1/2(d1d2) (1 half or 0.5 times diagonal 1 times diagonal 2)* * * * *The third option is s^2*sin(A) where s is the side length and A is an angle. It all depends on what information you are given.Area of Rhombus = length of first diagonal x length of second diagonal / 2
What is the area in terms of x of a rhombus with one diagonal that is 4 times the other diagonal?
Diagonals of a rhombus are perpendicular so the product is the area. If x is the smaller diagonal, the longer is 4x, and the area if 4x2.
How do I find a missing diagonal in a rhombus?
The answer depends on what information you do have about the rhombus. Assuming that you know the length of the sides and one of the diagonals, then,In the triangle formed by the given diagonal and the sides of the rhombus, you know all three sides. So you can use the cosine rule to calculate the angle between the sides of the rhombus.The other pair of angles in the rhombus are its supplement.So now you know two sides and the included angle of the triangle formed by the missing diagonal and the sides of the rhombus.You can use the cosine rule again to find the missing diagonal.
What quadrilaterals have diagonal that bisect each other?
A parallelogram a rectangle a square and a rhombus
The perimeter of a rhombus is 40cm and the length of one diagonal is 16cm find the length of the other diagonal?
The length of the other diagonal works out as 12cm
What is the formula for a rhombus in math?
Area=ba where b=base (any side), and a=altitude, the perpendicular length from the base to the opposite sideORArea= (d1*d2)/2 where d1 is the diagonal and d2 is the other diagonal
What is the area of rhombus one side of which measures 20cm and one diagonal 24 cm?
That will depend on the length of the other diagonal because area of a rhombus is 0.5*product of its diagonals.
What is a diagonal property of rhombus?
The diagonals of a rhombus are perpendicular and intersect each other at right angles which is 90 degrees
What is the area of a rhombus with a perimeter of 20 meters and a diagonal of 8 meters?
Constructing the figure, we find the other diagonal to have length 10.The area of the rhombus would thus be 10x8x0.5=40
What are the diagonals of rhombus?
One diagonal of a rhombus is larger than the other diagonal but both diagonals intercept each other at right angles.
What is the missing diagonal of a rhombus if the area is 120ft2 and the other diagonal is 16 feet?
Given: The area of the rhombus is 120 square feet The diagonal of the rhombus is 16 feet think of the rhombus being two identical triangles, connected at their base which is 16 feet long. Each of them would then have an area of 60 feet. Now, in a triangle, area = (base * height) / 2 the area is already given as 60, and the base as 16 we can say then: 60 = (16 * h) / 2 ∴60 = 8h ∴h = 7.5 Now, that 7.5 is half the length of the rhombus (as it's the height of one of our triangles, which each are half our rhombus). So we know that that the other diagonal on the rhombus is twice that. In other words, the answer is 15.
Similarities and differences of a square and rhombus?
The main difference between a square and a rhombus is that a square has all its angles equal to 90 degrees and a rhombus does not. A square has 4 lines of symmetry while rhombus only has 2. The diagonal lengths of a square are of the same measure. Rhombus diagonal lengths are of different measures. They are both a quadrilateral, all sides are equal in length, and opposite sides are parallel to each other.
How do you find the area of a rhombus?
Area = base x height.This formula also works for parallelograms, rectangles and squares.You find the area of a rhombus by multiplying l times h (length times height) where the height means the perpendicular distance from one side of length l to the other side.There are three ways to find the area of a rhombus, but these two ways are the easiest.You can use A = ba (base times altitude/height)You can use A= 1/2(d1d2) (1 half or 0.5 times diagonal 1 times diagonal 2)* * * * *The third option is s^2*sin(A) where s is the side length and A is an angle. It all depends on what information you are given.Area of Rhombus = length of first diagonal x length of second diagonal / 2
What is the area in terms of x of a rhombus with one diagonal that is 4 times the other diagonal?
Diagonals of a rhombus are perpendicular so the product is the area. If x is the smaller diagonal, the longer is 4x, and the area if 4x2.
How do I find a missing diagonal in a rhombus?
The answer depends on what information you do have about the rhombus. Assuming that you know the length of the sides and one of the diagonals, then,In the triangle formed by the given diagonal and the sides of the rhombus, you know all three sides. So you can use the cosine rule to calculate the angle between the sides of the rhombus.The other pair of angles in the rhombus are its supplement.So now you know two sides and the included angle of the triangle formed by the missing diagonal and the sides of the rhombus.You can use the cosine rule again to find the missing diagonal.
How do you find the angles of a Rhombus given that one diagonal is equal to one of its side?
The important property of a rhombus to note is that a rhombus has all sides of equal length. Then: Let the vertices be A, B, C, D; let the diagonal BD be the same length as the sides. Consider the triangle ABD formed by two sides of the rhombus and the diagonal BD. As all sides are equal in length, it must be an equilateral triangle and thus each angle can be calculated, in particular angle BAD of the rhombus. Consider the triangle BCD formed by the other two sides of the rhombus and the diagonal BD. The angle BCD of the rhombus can also be calculated as above. For angles ABC and CDA of the rhombus, note that angle ABC is the same as the sum of angles ABD and DBC. and those angles can be calculated above; similarly for angle CDA. A short cut that can be used is the property of a rhombus that opposite angles of a rhombus are equal which means once angle DAB has been calculate, BCD is then known. Then by subtracting the sum of these from 360o (the sum of the angles of a quadrilateral and a rhombus is an quadrilateral) and dividing the result by 2 will give the other two angles..
