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Question Video: Finding the Areas of Rhombuses Mathematics • 6th Grade

A diagonal of a rhombus has length 2.1, while the other one is four times as long. What is its area?

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Video Transcript

A diagonal of a rhombus has length 2.1, while the other one is four times as long. What is its area?

We start by remembering that a rhombus is a quadrilateral with all four sides equal in length. So, when we model our rhombus, we’ll need to have four equal sides. Instead of being given any information about the length of the sides of this rhombus, we’re given information about the diagonals. We’re given that one of these diagonals has a length of 2.1 units, and the other one is four times as long. Four multiplied by 2.1 will give us 8.4. Looking at our diagram, we can see that there’s a shorter diagonal and a longer diagonal. And therefore, the shorter one will be 2.1 units, and the longer one will be 8.4 units.

There are two formulas that we can use to find the area of a rhombus. One involves the base and the perpendicular height, and the other one involves the diagonals. As we’re only given the length of the diagonals here, it would be sensible to use that formula. So, we remember that the area of a rhombus is equal to 𝑑 sub one multiplied by 𝑑 sub two over two, where 𝑑 sub one and 𝑑 sub two are the lengths of the two diagonals. We can plug in the values of our two diagonals to give us 2.1 multiplied by 8.4 over two.

Simplifying our calculation, we’ll need to work out 2.1 multiplied by 4.2, which we can do without a calculator. We work out 21 multiplied by 42 using whatever multiplication method we choose. And then, as our two values had a total of two decimal places, then so will our answer. We weren’t given any length units in the question, but as we’ve worked out an area, we would be using square units. And so, our answer is that the area of this rhombus is 8.82 square units.

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