### 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.

**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 =
pq 2 - 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)p4 100 - The new length of the diagonal AC = q - q ×

= q - 0.04q = (1 - 0.04)q4 100 - Now, the area of the rhombus =
(1 + 0.04)p × (1 - 0.04)q 2

=(1 ^{2}- 0.04^{2})pq2 **...[Since, (a + b)(a - b) = a**^{2}- b^{2}]

=pq - 0.0016pq 2 - Change in area = New area of the rhombus - The area of the rhombus

=

-pq - 0.0016pq 2 pq 2

=pq - 0.0016pq - pq 2

=-0.0016pq 2 - % Change in area =

× 100Change in area The area of the rhombus

=

× 100-0.0016pq 2 pq 2

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