Subjects geometry

Sum Rhombus E68A04

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1. The problem is to find the sum of the rhombus, which typically means finding the sum of its diagonals or perimeter depending on context. Here, we clarify the sum of the diagonals. 2. A rhombus is a quadrilateral with all sides equal and its diagonals bisect each other at right angles. 3. The formula for the area of a rhombus is $$\text{Area} = \frac{d_1 \times d_2}{2}$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 4. If the problem asks for the sum of the diagonals, it is simply $$d_1 + d_2$$. 5. Without specific values, the sum of the diagonals is expressed as $$d_1 + d_2$$. 6. If you have the side length $s$ and one diagonal $d_1$, you can find the other diagonal $d_2$ using the Pythagorean theorem because the diagonals bisect each other at right angles: $$\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = s^2$$ 7. Rearranged to find $d_2$: $$d_2 = 2 \sqrt{s^2 - \left(\frac{d_1}{2}\right)^2}$$ 8. Then sum is: $$d_1 + d_2 = d_1 + 2 \sqrt{s^2 - \left(\frac{d_1}{2}\right)^2}$$ This is the general approach to find the sum of the diagonals of a rhombus.