The diagonal of a rhombus are of lengths 8cm and 4cm. Find the length of its side and area of it.
To find the length of the side and area of a rhombus, we'll use the given information that the diagonals are of lengths 8cm and 4cm.
Step 1: Recall the properties of a rhombus:
- A rhombus is a quadrilateral with all four sides of equal length.
- The diagonals of a rhombus bisect each other at right angles.
- The length of the diagonals of a rhombus is not equal unless the rhombus is a square.
Step 2: Determine the length of the side:
Since the diagonals of a rhombus bisect each other at right angles, we can form two right-angled triangles. Let's consider one of these triangles.
Let the length of the side of the rhombus be 'a'.
Using the Pythagorean theorem, we can find the length 'a'.
The given diagonals are 8cm and 4cm. In a right-angled triangle, the hypotenuse is the longest side, which corresponds to the diagonal. The other two sides are the lengths of the sides of the rhombus.
Using the Pythagorean theorem, we have:
(diagonal/2)^2 = (side/2)^2 + (side/2)^2
For the larger diagonal (8cm):
(8/2)^2 = (a/2)^2 + (a/2)^2
16 = 2(a/2)^2
16 = 2(a^2/4)
16 = (2/4) a^2
16 = (1/2) a^2
a^2 = 32
a ≈ √32
a ≈ 5.66 cm
Hence, the length of each side of the rhombus is approximately 5.66 cm.
Step 3: Calculate the area:
The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
In this case, d1 = 8 cm and d2 = 4 cm. Plugging these values into the formula:
Area = (8 * 4) / 2
Area = 32 / 2
Area = 16 square cm
Therefore, the length of each side of the rhombus is approximately 5.66 cm, and the area of the rhombus is 16 square cm.