Question

the four sides and one diagonal of a rhombus each have sides 2sqrt3 cm long. find the area of the rhombus, in cm?

Answer 1

The area of the rhombus is
`\(12 \, \text{cm}^2\).`The relationship between the diagonals in a rhombus aids in deriving the area, which, in this case, equates to
`\(12 \, \text{cm}^2\).`

Explanation:

The area of a rhombus can be calculated using the formula
`\( \text{Area} = (d_1 * d_2)/(2) \), where \(d_1\) and \(d_2\)`represent the lengths of the diagonals. Given that the length of one diagonal is
`\(2√(3)\`) cm and all sides are also
`\(2√(3)\)` cm each, the diagonals form right angles. Thus, using the Pythagorean theorem, the length of the other diagonal is found to be \(4\) cm. Plugging these values into the formula yields
`\( \text{Area} = (2√(3) * 4)/(2) = 12 \, \text{cm}^2\).`

The area of a rhombus can be determined by dividing the product of its diagonals by 2. Given that the rhombus has sides of
`\(2√(3)\)` cm each, implying the diagonals are perpendicular to each other, the Pythagorean theorem helps find the length of the other diagonal. By substituting the diagonal lengths into the area formula, the calculation yields an area of
`\(12 \, \text{cm}^2\),`representing the total surface space enclosed by the rhombus. The relationship between the diagonals in a rhombus aids in deriving the area, which, in this case, equates to
`\(12 \, \text{cm}^2\).`