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
40.26 units²
48.92 units²
76.44 units²

Explanation:

Step1: Find area of one sector (triangle)

The area of a triangle is given by the formula \( A = \frac{1}{2} \times \text{base} \times \text{height} \). For one sector (treated as a triangle), the base is \( 1.56 \) units and the height is \( 3.92 \) units. So, the area of one sector is \( \frac{1}{2} \times 1.56 \times 3.92 \).
\[
\frac{1}{2} \times 1.56 \times 3.92 = 0.78 \times 3.92 = 3.0576
\]

Step2: Find total area of the circle

Since the circle is dissected into 16 congruent sectors, the total area of the circle is 16 times the area of one sector. So, we multiply the area of one sector by 16: \( 16 \times 3.0576 \).
\[
16 \times 3.0576 = 48.9216 \approx 48.92
\]

Answer:

\( 48.92 \) units² (corresponding to the option with this value, likely the third option presented as 48.92 units²)