Question

whats the area of an ellipse with the major axis 20 m and the minor axis 10 m? round your answer to the nearest whole number. a) 50 m² b) 314 m² c) 200 m² d) 157 m²

Explanation:

Step1: Recall the formula for the area of an ellipse

The formula for the area of an ellipse is \(A=\pi ab\), where \(a\) is the semi - major axis and \(b\) is the semi - minor axis.

Step2: Calculate the semi - axes

Given the major axis \(= 20m\), so the semi - major axis \(a=\frac{20}{2}=10m\). Given the minor axis \(= 10m\), so the semi - minor axis \(b = \frac{10}{2}=5m\).

Step3: Substitute into the formula

Substitute \(a = 10\) and \(b=5\) into \(A=\pi ab\). Then \(A=\pi\times10\times5=50\pi\).

Step4: Calculate the numerical value

Since \(\pi\approx3.14\), then \(A = 50\times3.14=157m^{2}\).

Answer:

D) \(157m^{2}\)