1. A rhombus has an area of 5 square meters and a length of 3 meters. In a similar rhombus, the length of a side is 9 meters. What is the area of the second rhombus?

[Area= diagonal1 X diagonal2 / 2]

To find the area of the second rhombus, we need to use the formula:

Area = (Diagonal 1 * Diagonal 2) / 2

In the given question, we are not given the lengths of the diagonals directly. However, we are given the lengths of the sides of both rhombuses.

For a rhombus, the diagonals bisect each other at right angles and divide the rhombus into four congruent triangles. The diagonals are not necessarily the same length as the sides.

To find the lengths of the diagonals in the second rhombus, we can use the fact that the ratio of the lengths of corresponding sides in similar shapes is the same.

Let's calculate the ratio of the side lengths in the two rhombuses:

Ratio of side lengths = (side length of second rhombus) / (side length of first rhombus)
= 9 meters / 3 meters
= 3

Since both rhombuses are similar, the ratio of their side lengths will be the same as the ratio of their diagonal lengths.

Let's find the length of the diagonals in the second rhombus:

Diagonal 1 of second rhombus = (Diagonal 1 of first rhombus) * (ratio of side lengths)
= 3 meters * 3
= 9 meters

Diagonal 2 of second rhombus = (Diagonal 2 of first rhombus) * (ratio of side lengths)
= 3 meters * 3
= 9 meters

Now, we can plug in the values for the diagonals into the formula to find the area of the second rhombus:

Area = (Diagonal 1 * Diagonal 2) / 2
= (9 meters * 9 meters) / 2
= (81 square meters) / 2
= 40.5 square meters

Therefore, the area of the second rhombus is 40.5 square meters.

3 times the side, 9 times the area