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How do you find the area of a rhombus with only its diagonal given?
Wiki User
∙ 12y ago
Assuming you have a rhombus SRQP, where PR and QS are the diagonals, you find the area by determining the area of the two triangles PQR and PRS, and adding them together.
The formula for finding the area of a triangle is (1/2)*base*height.
In our two triangles, the height is represented by 1/2 the length of SQ. In most math texts, this segment is referred to as y. PR (the other diagonal) is referred to as x.
For our purposes, the base of our triangles are both x. The height is one half of SQ, or y/2.
Area = (1/2)x * y/2 + (1/2)x * y/2
Simplify
Area = (xy/4) + (xy/4)
Combine those...
Area = 2xy/4
Simplify again
Area = (1/2)xy
Or
xy/2
QED
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∙ 12y ago
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How do you find the perimeter of a rhombus when area is given?
There is no relationship between the perimeter and the area of a rhombus. Take a rhombus with all 4 sides = 2 units. Therefore the perimeter is 8 units. There are an infinite number of possible areas for this rhombus. The largest possible area will be when the rhombus approaches the shape of a square = 4 square units. The smallest area will be when the one diagonal approaches 0 units and the other diagonal approaches 4 units (squashed almost flat). So two very extreme areas can have the same perimeter, including all those areas in-between.
How do you find the area of a parallelogram if only the diagonal is given?
You cannot. There is not enough information.
Area of rhombus if area and perimeter is given and if you have to find altitude?
Perimeter = 4*Side so that Side = Perimeter/4 Area of a rhombus = Side * Altitude so Altitude = Area/Side = Area/(Perimeter/4) = 4*Area/Perimeter
Can you find the area of a rectangle if the problem doesn't show you the base and height?
The one alternative to find the area of a rectangle is when you are given the length of one diagonal and its slope.
How do you find the area of a rectangle when one diagonal is given?
Divide the rectangle in two triangles and then use the pythagorean theorem to find the remaining sides.
How do I find the area of a rhombus with just one diagonal?
If side is given too, then you can find area with one diagonal. As diagonals bisect each other in a rhombus at 90°, Using Pythogoras Theorem: (Half d1)² = (side)² - (Half d2)²
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
Find the area of the rhombus whose perimeter is 80m and one of whose diagonal is 24?
123
Find the area of the rhombus below?
The answer is given below.
How do you find the perimeter of a rhombus when area is given?
There is no relationship between the perimeter and the area of a rhombus. Take a rhombus with all 4 sides = 2 units. Therefore the perimeter is 8 units. There are an infinite number of possible areas for this rhombus. The largest possible area will be when the rhombus approaches the shape of a square = 4 square units. The smallest area will be when the one diagonal approaches 0 units and the other diagonal approaches 4 units (squashed almost flat). So two very extreme areas can have the same perimeter, including all those areas in-between.
There is a yellow rhombus on the flag of Brazil The long diagonal on the rhombus measures 7.0 units The short diagonal on the rhombus measures 4.4 units The area of any rhombus is half the product?
That is one of the ways of finding the area of a rhombus. The area is half the product of the diagonals. In this case, 1/2 of 7 x 4.4 or .154. You can also find the area of a rhombus by using one side as the base and finding an altitude for that base and multiplying them. There is a third way using trigonometry.
How do you find the area of a parallelogram if only the diagonal is given?
You cannot. There is not enough information.
How do you find the area of a square given only the length of its diagonal?
Given the length of the diagonal of the square ... call it 'D units'. The area of the square is (1/2 D2) (same units)2.
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
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 is the area of rhombus DEFG if DF is 10 and EF is 11?
If those are its diagonals then area is: 0.5*10*11 = 55 square units other wise use Pythagoras to find diagonal EG because area of a rhombus is 0.5 times the product of its diagonals.
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?
Rhombus Area = side x height = 6 cm x 4 cm = 24 cm2In 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 thatthe 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] ≈ 4.3Thus, the length of the other diagonal of the rhombus is about 4.3 cm long.
