Question Video: Finding the Diagonal Length of a Square given Its Area Mathematics • 6th Grade

Video Transcript

What is the diagonal of a square of area 942? Round your answer to the nearest hundredth.

We can begin this question by recalling some of the key properties of a square. Each side of a square is equal in length. If we let the length of each side of a square be 𝐿 units, the area will be equal to 𝐿 squared. In this question, we are told that the area is equal to 942. Therefore, 𝐿 squared equals 942. We want to calculate the length of the diagonal of the square which we will call 𝑑. Whilst we might be tempted to calculate the length of the square, a better and more efficient way would be to recall the Pythagorean theorem. This states that 𝑎 squared plus 𝑏 squared is equal to 𝑐 squared, where 𝑐 is equal to the longest side of a right-angle triangle known as the hypotenuse.

In the square drawn, 𝐿 squared plus 𝐿 squared is equal to 𝑑 squared. Simplifying the left-hand side gives us two 𝐿 squared. We can then divide both sides of this equation by two such that 𝐿 squared is equal to 𝑑 squared over two. We can then substitute this into our first equation. If 𝐿 squared is equal to 942, then 𝑑 squared over two must be equal to 942. We can multiply both sides of this equation by two such that 𝑑 squared is equal to 1884. Finally, we can square root both sides such that 𝑑 is equal to 43.4050 and so on.

We are asked to round to the nearest hundredth, which is the same as rounding to two decimal places. If our deciding number is five or greater, we round up, which means that the diagonal of the square is 43.41. There were no units given in this question, so this is the final answer.