Video Transcript
Find the difference between the area of a square whose diagonal length is six decimeters and that of a parallelogram whose base length is six centimeters and height is seven centimeters.
Let’s begin by recalling how we calculate the area of a square and the area of a parallelogram. If we have a square of length 𝐿 units, its area is equal to 𝐿 squared. The area of a parallelogram is equal to the base multiplied by its perpendicular height. We are also asked to consider the diagonal length of the square. Using the Pythagorean theorem 𝑎 squared plus 𝑏 squared equals 𝑐 squared, where 𝑐 is the length of the longest side of a right-angle triangle known as the hypotenuse, we know that 𝐿 squared plus 𝐿 squared is equal to 𝑑 squared. The left-hand side simplifies to two 𝐿 squared. Dividing both sides of this equation by two gives us 𝐿 squared is equal to 𝑑 squared divided by two. This means that the area of a square is equal to its diagonal squared divided by two.
Let’s now consider the measurements we are given in this question. We recall that one decimeter is equal to 10 centimeters and we are told the diagonal of the square is six decimeters. This means the diagonal of the square is also equal to 60 centimeters. We can calculate the area of the square by squaring 60 and then dividing by two. 60 squared is equal to 3600. Dividing this by two gives us 1800. The area of the square is 1800 square centimeters. The base of the parallelogram is six centimeters long and its height is seven centimeters. This means that the area is equal to six multiplied by seven. This is equal to 42, so the area of the parallelogram is 42 square centimeters.
We are asked to calculate the difference between the areas. We need to subtract 42 from 1800. This is equal to 1758. The difference between the area of the square and that of the parallelogram is 1758 square centimeters.
