A rhombus has a side that is 14cm long. One of its diagonals is 24cm long. What is the area?
To find the area of a rhombus, we can use the formula: Area = (diagonal 1 * diagonal 2) / 2.
In this case, we have the length of one side and the length of one diagonal. To find the length of the other diagonal, we can use the properties of a rhombus.
Since a rhombus has opposite sides that are equal in length, and the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of the other diagonal:
Let A, B, C, and D be the four corners of the rhombus, with AD and BC being the diagonals.
We know that AD = 24cm and AB = 14cm (the given side length). Let's denote the midpoint of AB as M. Now, we have a right triangle ADM, where DM is perpendicular to AB.
Using the Pythagorean theorem, we can find the length of DM:
DM^2 + AM^2 = AD^2
Since AM is half the length of AB, we have:
DM^2 + (14/2)^2 = 24^2
DM^2 + 7^2 = 24^2
DM^2 + 49 = 576
DM^2 = 576 - 49
DM^2 = 527
DM ≈ √527
Now that we have the length of both diagonals, we can calculate the area of the rhombus:
Area = (diagonal 1 * diagonal 2) / 2
Area = (24cm * √527cm) / 2
Area ≈ (24 * √527) / 2
Area ≈ 12 * √527
Therefore, the area of the rhombus is approximately 12 times the square root of 527 square centimeters.
Draw a rhombus, and mark one side as 24 cm, and one of the diagonals as 24 cm long. Then the half diagonal is 12 cm.
Since the diagonals of a rhombus intersect at right angles, we have a right-triangle with hypotenuse 14 cm, with one side as 12. The other half-diagonal is therefore
sqrt(14²-12²)=sqrt(52).
The area of a rhombus is the product of the diagonals (24 cm and 2sqrt(52)) divided by 2.