Find the area of a rhombus with a perimeter of 20 meters and a diagonal of 8 meters
All four sides are equal, so each side is 5 m.
Also the diagonals right-bisect each other to form 4 congruent right-angled triangles
Consider one of thes.
The hypotenuse is 5, one leg is 4 , so the other must be 3 by Pythagoras.
Area of one of those = (1/2)(3)(4) = 6
So the whole rhombus has area of 24 m^2
or
the area of a rhomus = (1/2)(product of their diagonals)
= (1/2)(6)(8) = 24
The perimeter of a rhombus is 40 cm and the distance between a pair of parallel side is 5.6 cm. If the length of one of its diagonals is 7 cm, find the length of the other diagonal.
To find the area of a rhombus, we can use the formula:
Area = (1/2) * product of diagonals
In this case, we are given the perimeter and one diagonal. Let's call the other diagonal "d2".
Given:
Perimeter = 20 meters
Diagonal (d1) = 8 meters
We know that the perimeter of a rhombus is the sum of all four sides, so each side of the rhombus will be (20 / 4 = 5 meters).
Now, let's find the other diagonal (d2) using the Pythagorean theorem.
Using the Pythagorean theorem, we know that the diagonals of a rhombus bisect each other at right angles, creating four right triangles. So, we have:
d1/2 = d2/2 = 5/2 = 2.5 meters
Now, we can calculate the area of the rhombus:
Area = (1/2) * d1 * d2
= (1/2) * 8 * 2.5
= 4 * 2.5
= 10 square meters
Therefore, the area of the rhombus is 10 square meters.
To find the area of a rhombus, you need to know the length of one of its diagonals. The diagonal of a rhombus divides it into two congruent right triangles. We can use the Pythagorean theorem to find the length of each side of the right triangle.
Let's call the diagonal of the rhombus "d" and the length of one of its sides "s". In a rhombus, all four sides have the same length.
Given that the perimeter of the rhombus is 20 meters, we know that the sum of all four sides is equal to 20:
4s = 20
Dividing both sides by 4, we get:
s = 5
Now, let's find the length of the other side of the right triangle. Since the diagonal divides the rhombus into two congruent right triangles, we can determine the length of the other side of the right triangle by using the Pythagorean theorem.
In our case, the diagonal "d" is 8 meters, and one side of the right triangle, "s," is 5 meters. Let's call the length of the other side of the right triangle "a".
Using the Pythagorean theorem:
d^2 = s^2 + a^2
8^2 = 5^2 + a^2
64 = 25 + a^2
Subtracting 25 from both sides, we have:
39 = a^2
Taking the square root of both sides, we get:
a ≈ 6.24
Now that we know the length of the other side of the right triangle, we can calculate the area of one of the triangles using the formula for the area of a triangle:
Area = (base × height) / 2
In this case, the base of the triangle is equal to "s" (5 meters) and the height is equal to "a" (6.24 meters):
Area = (5 × 6.24) / 2
Area ≈ 15.6 square meters
Since the area of the rhombus is twice the area of one of the triangles, the area of the rhombus is:
Area of rhombus = 2 × 15.6
Area of rhombus ≈ 31.2 square meters
Therefore, the area of the given rhombus is approximately 31.2 square meters.