Q&A for How to Calculate the Area of a Rhombus

Perimeter = sum of all sides. The rhombus has equal sides, so its perimeter = side x 4.

In a rhombus, the diagonals bisect and are perpendicular, meaning that inside the rhombus there are four right-angle triangles, with side lengths half that of the diagonals, use the pythagoran theorem to find the hypotenuses a² + b² = c² Now we have the base, given any of the angles inside the rhombus, we can find all of them because they are corresponding and all add up to 360 degrees, once we have all of the angles, another two identical triangles appear. we only have to use one of these as they are identical. Now we have the hypotenuse and an angle of this triangle so using trigonometry we can find the adjacent side which is the height of the rhombus.

Use the Pythagorean theorem to find the sides and then find the perimeter.

Since the area equals the product of the base and the altitude (height), divide the area by the height to get the base (side).

For ANY shape, the formula for calculating the sum of the interior angles when the number of sides = "s" is: (s - 2) x 180 So, a triangle for example is 3 - 2 x 180 = 1 x 180 = 180. A quadrilateral is 4 - 2 x 180 = 2 x 180 = 360. A pentagon is 5 - 2 x 180 = 3 x 180 = 540, and so on.

If you have the diagonals, you can use the Pythagorean Theorem. Let's say d is the first diagonal and g is the second. The formula for one side is (square root of ((1/2d)^2+(1/2g)^2))).

Find the other side using Pythagoras theorem. Other diagonal=8*2=16 cm. Area of rhombus=1/2 *product of diagonals=1/2*16*12=96 sq.cm.

You can't find the area with the information you have. Either you need the length of each diagonal (which you don't have), or you need the base and the height. You have the base, but you don't have the height.

Cut the rhombus in half to get one diagonal, then you can use pythagoras (a² + b² = c²) to get the length of that diagonal. then cut it in half again and do the same for the other diagonal.

Because a rhombus has four equal sides, divide the perimeter by 4 to get the length of the base, then divide that into the area to get the altitude.

Let d be the length of the shorter diagonal. Then 2d is the length of the longer diagonal. The area is 169 = (d x 2d) / 2 = 2d² / 2 = d². Then d = √169 = 13. So the diagonals are 13 cm and 26 cm.

Divide the perimeter by 4. That's the base. Divide the area by the base. That's the altitude.

The area is the base multiplied by the height.

You would also have to know the interior angles.

The area of a rhombus is half the product of its diagonals. Therefore, the length of one of the diagonals is equal to twice the area divided by the length of the other diagonal. Twice the area of this rhombus is 120 cm². Dividing 120 cm² by 12 cm results in the other diagonal being 10 cm long.

You would also have to know the interior angles.

See [[Find the Area of a Quadrilateral]].

As the area of rhombus is 1/2× product of diagonals, we can use transposing method, say, the area is 48cm so it will be 1/2× (x × y) = 48, (x × y )= 48 × 2 =96 and as you said that the diagonals are same that the answer would be under root 96, which is 9.797.

If it doesn't clarify that the sides are given and you have to find angle of rhombus, it totally depends on the figure. In this case, you can measure the angle of the given figure sides but not predict the angle by its sides without a reference figure.

Double the area, then divide by the length of the known diagonal.

1). 104/4 = 26 (side of rhombus) 2). 48/2 =24 to use the Pythagoras theory 26²-24²=100 SQR(100)=10 3). 10x2 =20 (2nd diagonal). 3). (d1.d2)/2 => 20*48/2 = 480cm².

Multiply the length of one side by 4.

You can't do it. You need more information, such as the height of the rhombus or the size of its angles.

Divide the area by the height: 180 cm² / 12 cm = 15 cm. That's the length of the base. Multiply the base by 4: (15 cm)(4) = 60 cm. That's the perimeter.

Because sides B and D are defined as being opposite and equal in length to each other in ABCD, angles b and d are opposite and equal to each other. Then ( b + d) = 2b = 2d = 160°, and b and d are each equal to 80°. The sum of all four interior angles of a rhombus is (2)(180°) = 360°. Subtract the sum of b and d from 360° to get 200°, which is the sum of the other two angles, a and c, which are equal to each other. So a + c = 2a = 2c = 200°. So a and c are each equal to 100°.

Let d equal the unknown diagonal. The area is (side)(altitude) = (6 cm)(4 cm) = 24 sq cm. The area also equals one-half the product of the diagonals. So 24 = (8)(d) / 2 = 4d. Divide both sides by 4: d = 6 cm.