A rhombus shaped fountain has diagonals that measure 8.4 meters and 10.2 meters. What is the area of the rhombus?
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Answer:
Estimations of π/4:
100 points: 0.75
1,000 points: 0.768
10,000 points: 0.7819
Step-by-step explanation:
To get an estimate of π/4 you can place random points in the square [0, 1] × [0, 1] and estimate it as the ratio of the points that landed inside the unit circle to the total number of points (because the ratio of the area of the circle to the area of the square is π/4).
We do it for 100 xy points and we get:
Point inside the circle area = 75
Estimation of π/4 = 0.75
We do it for 1,000 xy points and we get:
Point inside the circle area = 768
Estimation of π/4 = 0.768
If we do it fo 10,000 xy points, we get
Point inside the circle area = 768
Estimation of π/4 = 0.768
The value of π/4 (4 decimals) is 0.7854.
The simulation gets more precise with the increase in the number of points.
The spreadsheet and the graphs are attached.
