### If a rhombus is re-shaped such that one of its diagonal increases by 4%, while other diagonal decreases by 4%. Find the percentage change in the area of rhombus.

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**Answer: **0.16% decrease

**Step by Step Explanation: **

Let's assume the length of the diagonals BD and AC of the rhombus ABCD are **p** and **q** respectively.- The area of the rhombus =
- According to the question, one of its diagonal increases by 4%, while other diagonal decreases by 4%.

The new length of the diagonal BD = p + p × = p + 0.04p = (1 + 0.04)p - The new length of the diagonal AC = q - q × = q - 0.04q = (1 - 0.04)q
- Now, the area of the rhombus =
(1 + 0.04)p × (1 - 0.04)q |

2 |

= **...[Since, (a + b)(a - b) = a**^{2} - b^{2}]

= - Change in area = New area of the rhombus - The area of the rhombus

= -

=

= - % Change in area =
Change in area |

The area of the rhombus |

× 100

= × 100

= -0.16% - Thus, the area of the rhombus is decreased by 0.16%.