The side of a rhombus is 15 centimeters long, and the length of its longer diagonal is 24.6 centimeters. Find the area.
211.6 units squared
To find the area of a rhombus, you can use the formula:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
Given that the side length of the rhombus is 15 centimeters and the length of the longer diagonal is 24.6 centimeters, we need to find the length of the shorter diagonal.
Since a rhombus has two congruent diagonals that intersect at a 90-degree angle, we can divide the longer diagonal in half to find the length of the shorter diagonal.
Shorter diagonal = Longer diagonal / 2
Shorter diagonal = 24.6 / 2
Shorter diagonal = 12.3 centimeters
Now we have the lengths of both diagonals:
d1 = 12.3 centimeters
d2 = 24.6 centimeters
Plugging these values into the area formula:
Area = (12.3 * 24.6) / 2
Area = 302.58 / 2
Area = 151.29 square centimeters
Therefore, the area of the rhombus is 151.29 square centimeters.
To find the area of a rhombus, you need to know the length of one of its diagonals and the length of one of its sides. In this case, you are given the length of the side (15 cm) and the length of the longer diagonal (24.6 cm).
The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2. Therefore, the formula to find the area of a rhombus is:
Area = (diagonal1 * diagonal2) / 2
In this case, we only know the length of one diagonal (24.6 cm). To find the length of the other diagonal, we can use the Pythagorean Theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In a rhombus, the diagonals are perpendicular bisectors of each other, which means they form right angles where they intersect. So we can use the Pythagorean Theorem to find the length of the other diagonal. Let's call the length of the other diagonal "d":
d^2 = (15/2)^2 + (24.6/2)^2
d^2 = 7.5^2 + 12.3^2
d^2 = 56.25 + 151.29
d^2 = 207.54
d ≈ 14.4 cm
Now that we have both diagonals, we can calculate the area:
Area = (diagonal1 * diagonal2) / 2
Area = (14.4 * 24.6) / 2
Area = 354.24 / 2
Area ≈ 177.12 cm^2
Therefore, the area of the rhombus is approximately 177.12 square centimeters.
The diagonals in a rhombus right-bisect each other, giving you 4 identical right-angled triangles
look at one of them, the hypotenuse would be 15 and the other side is 12.3 , half the diagonal given.
Can you find the missing side using Pythagoras?
Find the area of one of the triangles , then multiply by 4