Question

a rectangle is inscribed in a circle such that the side lengths are 1.4 units and 5.3 units. which of the following, in square units, is nearest to the area of the circle?
o 12.7
o 17.2
o 20.2
o 23.6
o 40.7
question help: video
check answer

Explanation:

Step1: Find the diameter of the circle

The diameter of the circle is the diagonal of the rectangle. By the Pythagorean theorem, if the sides of the rectangle are \(a = 1.4\) and \(b=5.3\), then the diagonal \(d\) of the rectangle (diameter of the circle) is \(d=\sqrt{a^{2}+b^{2}}\). So \(d = \sqrt{1.4^{2}+5.3^{2}}=\sqrt{1.96 + 28.09}=\sqrt{30.05}\approx5.48\).

Step2: Find the radius of the circle

The radius \(r\) of the circle is \(r=\frac{d}{2}\), so \(r=\frac{5.48}{2}=2.74\).

Step3: Calculate the area of the circle

The area of a circle is \(A=\pi r^{2}\). Substituting \(r = 2.74\) into the formula, we get \(A=\pi\times(2.74)^{2}\approx3.14\times7.5076\approx23.6\).

Answer:

23.6