Question

a circle has been dissected into 16 congruent sectors. the base of one sector is 1.56 units, and its height is 3.92 units. using the area of a triangle formula, what is the approximate area of the circle? 27.52 units² 48.25 units² 48.92 units² 76.44 units²

Explanation:

Step1: Calculate the area of one sector

The area formula of a triangle is \(A=\frac{1}{2}\times base\times height\). Given \(base = 1.56\) units and \(height=3.92\) units.

$$A_{sector}=\frac{1}{2}\times1.56\times3.92$$

$$A_{sector}=0.78\times3.92 = 3.0576$$

Step2: Calculate the area of the circle

Since the circle is divided into 16 congruent sectors, the area of the circle \(A_{circle}=16\times A_{sector}\)

$$A_{circle}=16\times3.0576$$

$$A_{circle}=48.9216\approx48.92$$

Answer:

48.92 units²