the diagonals of a rhombus are 24 meter and 18 meter find the area,length of a side and perimeter?
To find the area, length of a side, and perimeter of a rhombus given the lengths of its diagonals, we can use the following formulas:
1. Area of a rhombus = (Product of the diagonals) / 2
2. Side length of a rhombus = (Square root of [(Diagonal 1)^2 + (Diagonal 2)^2]) / 2
3. Perimeter of a rhombus = 4 * (Side length)
Let's calculate the area, length of a side, and perimeter based on the given diagonal lengths:
1. Area of the rhombus = (24 * 18) / 2 = 432 square meters.
2. Side length of the rhombus = √[(24^2) + (18^2)] / 2
= √(576 + 324) / 2
= √900 / 2
= 30 / 2
= 15 meters.
3. Perimeter of the rhombus = 4 * (Side length)
= 4 * 15
= 60 meters.
Therefore, the area of the rhombus is 432 square meters, the length of each side is 15 meters, and the perimeter is 60 meters.
recall these properties:
-all sides of rhombus are equal.
-the diagonals of rhombus are perpendicular (forms four 90 degree angles)
-area of rhombus, if diagonals are given, can be calculated by
A = d1 * d2 /2
where d1 & d2 are the diagonal lengths
-side of a rhombus, if diagonals are given, can be calculated by
s = sqrt(d1^2 + d2^2)
*note that this is just pythagorean theorem
applying these,
A = 24*18/2
A = 216 m^2
s = sqrt(24^2 + 18^2)
s = sqrt(900)
s = 30 m
P = 4*s
P = 4*30
P = 120 m
hope this helps~ :)