what is the area of a rhombus if AB equals 9.9 and AC equals 13 and DB equals 15?
Since a rhombus has equal sides, the lines AC and BD intersect at right angles, dividing it into four congruent triangles.
The total area is (4)*(1/2)*(4.45)(6.5)
= (1/2)(9)(13) = 58.5
I misread the problem by using 9 for one of the diagonals. The answer should be
A = (1/2)(13)(15) = 97.5
Note that you not have to use the value of AB. Its value, for a true rhombus, should be sqrt[(6.5)^2 + (7.5)^2] = 9.92 , which is close to what was given.
To find the area of a rhombus, we need to use the formula:
Area = (diagonal1 * diagonal2) / 2
In this case, we are given the lengths of sides AB, AC, and DB, which are not the diagonals of the rhombus. However, we can use these side lengths to calculate the diagonals using the properties of a rhombus.
In a rhombus, the diagonals are perpendicular bisectors of each other and divide the rhombus into four congruent right-angled triangles.
To find the length of the diagonals, we can use the Pythagorean theorem.
Let's consider triangle ABC (where AB = 9.9 and AC = 13) with AB as the base and AC as the height. The diagonal is the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of diagonal BD:
BD^2 = AB^2 + AD^2
Since we know AB = 9.9 and AC = 13, we can rearrange the equation:
BD^2 = (9.9/2)^2 + 13^2
BD^2 = 4.95^2 + 13^2
BD^2 = 24.5025 + 169
BD^2 = 193.5025
Taking the square root of both sides, we find:
BD ≈ √193.5025 ≈ 13.911
Similarly, we can calculate the length of diagonal AC:
AC^2 = AB^2 + BC^2
Since we know AB = 9.9 and DB = 15, we can rearrange the equation:
AC^2 = (9.9/2)^2 + 15^2
AC^2 = 4.95^2 + 15^2
AC^2 = 24.5025 + 225
AC^2 = 249.5025
Taking the square root of both sides, we find:
AC ≈ √249.5025 ≈ 15.783
Now that we have the lengths of the diagonals, we can calculate the area of the rhombus using the formula:
Area = (diagonal1 * diagonal2) / 2
Area = (13.911 * 15.783) / 2
Area ≈ 218.875
Therefore, the approximate area of the rhombus is 218.875 square units.