Question

The points L ( − 7 , 9 ) (−7,9), M ( 0 , 5 ) (0,5), N ( 8 , 4 ) (8,4), and O ( 1 , 8 ) (1,8) form rhombus LMNO. Plot the points then click the "Graph Quadrilateral" button. Then find the area of the rhombus.

Answer 1

To find the area of the rhombus, we need to first find the length of one of its diagonals. We can use the distance formula to find the length of any of the four sides:

LM = sqrt[(0 - (-7))^2 + (5 - 9)^2] = sqrt[49 + 16] = sqrt[65]

NO = sqrt[(1 - 8)^2 + (8 - 4)^2] = sqrt[49 + 16] = sqrt[65]

So both diagonals have the same length, which means the rhombus is also a square. The length of each side is:

LM = NO = sqrt[65]

Now we can find the area of the rhombus by using the formula:

Area = (diagonal1 * diagonal2) / 2

Since the diagonals are equal, we can simplify this to:

Area = (diagonal)^2 / 2

Substituting in the value for the diagonal, we get:

Area = (sqrt[65])^2 / 2 = 65 / 2

So the area of the rhombus is 32.5 square units