Video Transcript
Determine the difference in area
between a square having a diagonal of 10 centimeters and a rhombus having diagonals
of two centimeters and 12 centimeters.
Although it’s not essential to
answering this problem, we’ll begin by sketching the two shapes. We have a square with a diagonal of
length 10 centimeters and a rhombus with diagonals of lengths two centimeters and 12
centimeters. We then need to recall how to find
the area of each of these shapes from the length of their diagonal. The area of a square with a
diagonal of length 𝑑 units is 𝑑 squared over two. The area is half the square of the
length of the diagonal. So the area of this square, which
has a diagonal of 10 centimeters, is 10 squared over two. That’s 100 over two, which is 50
square centimeters.
The area of a rhombus, on the other
hand, with diagonals of lengths 𝑑 one and 𝑑 two is 𝑑 one multiplied by 𝑑 two
over two. It’s half the product of the
lengths of its diagonals. So the area of this rhombus, which
has diagonals of lengths 12 centimeters and two centimeters, is 12 multiplied by two
over two, which simplifies to 12 square centimeters. To find the difference in area, we
subtract the area of the smaller shape, that’s the rhombus, from the area of the
larger shape, that’s the square, 50 minus 12, which gives a difference in area of 38
square centimeters.
