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How do you calculate the area of a rhombus?

To calculate the area of a rhombus, you can use the formula:

Area=d1×d22\text{Area} = \frac{d_1 \times d_2}{2}

A rhombus is a special type of quadrilateral where all four sides are of equal length. One of its defining characteristics is that the diagonals bisect each other at right angles (90 degrees). These diagonals play a crucial role in determining the area of the rhombus. The area formula is derived from the properties of these diagonals. Specifically, if you know the lengths of the diagonals, denoted as d1d_1 and d2d_2, you can calculate the area by multiplying these lengths together and then dividing the product by 22.

For instance, if the lengths of the diagonals are 8cm8 \, \text{cm} and 6cm6 \, \text{cm}, you would compute the area as follows:

Area=8cm×6cm2=48cm22=24cm2.\text{Area} = \frac{8 \, \text{cm} \times 6 \, \text{cm}}{2} = \frac{48 \, \text{cm}^2}{2} = 24 \, \text{cm}^2.

This calculation is valid because the diagonals of a rhombus divide it into four right-angled triangles, and the total area of the rhombus is equal to the sum of the areas of these triangles.

Alternatively, if you know the base and height of the rhombus, you can also apply the formula:

Area=base×height.\text{Area} = \text{base} \times \text{height}.

However, using the diagonals is often more straightforward, especially when their lengths are readily available or easily measurable. Familiarizing yourself with these methods will enhance your ability to solve problems related to the area of a rhombus in your GCSE Maths exams.

Answered by: Prof. David Martin
A-Level Physics Tutor
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