Find the area of the rhombus: In rhombus ABCD, AB=11 and AC=13. Find the area of the rhombus.
What should be done to find the values of the diagonals?
A = D1*D2/2 = 13 * 13 / 2 =84.5
All of the sides of a rhombus are equal. So the longest side is the diagonal.
CORRECTION!
The 2 diagonals are NOT equal. But they
are perpendicular bisectors of each other. They intersect at E.
(AE)^2 + (BE)^2 = (11)^2,
(6.5)^2 + (BE)^2 = 121,
42.25 + (BE)^2 = 121,
(BE)^2 = 121 - 42.25 = 78.75,
BE = sqrt(78.75) = 8.9.
BD = 2 * BE = 2 * 8.9 = 17.8.
A = D1 * D2 / 2 = 13 * 8.9 / 2 = 57.85
OOPS!
A = D1 * D2 / 2 = 13 * 17.8 /2 = 115.7
To find the values of the diagonals in a rhombus, you can use the Pythagorean theorem. Generally, a rhombus has two diagonals that intersect each other at a 90-degree angle, forming four congruent right triangles. The diagonals of a rhombus are also perpendicular bisectors of each other, meaning they divide each other into two equal parts.
In this specific case, the given information includes the length of sides AB and AC. To find the values of the diagonals, we can use the Pythagorean theorem.
Step 1: Draw rhombus ABCD and label the given lengths as AB = 11 and AC = 13.
Step 2: Since the diagonals of a rhombus bisect each other, let's label the intersection point of the diagonals as E.
Step 3: Use the Pythagorean theorem to find the length of diagonal BD. In right triangle ABE, where AE is a segment of length 11 and AB is a segment of length BD/2, we can apply the Pythagorean theorem:
(BD/2)^2 = AE^2 + AB^2
(BD/2)^2 = 11^2 + (BD/2)^2
Simplifying, we get:
BD^2/4 = 121 + BD^2/4
Now, isolate BD^2 by multiplying both sides of the equation by 4:
BD^2 = 484 + BD^2
Combine like terms:
0 = 484
This equation is inconsistent and has no solution. It means that there is an error in the given information or the problem statement.
Therefore, given the information provided, it is not possible to find the area of the rhombus.