Question

question 4 (multiple choice worth 2 points)
(06.01 mc)
a circle has been dissected into 16 congruent sectors. the base of one sector is 1.17 units, and its height is 2.94 units. using the area of a triangle formula, what is the approximate area of the circle?
o 27.14 units²
o 27.32 units²
o 49.22 units²
o 54.14 units²

Explanation:

Step1: Find area of one sector

The area of a triangle (sector approximated as triangle) is given by \( A = \frac{1}{2} \times b \times h \). Here, base \( b = 1.17 \) units and height \( h = 2.94 \) units. So, area of one sector is \( \frac{1}{2} \times 1.17 \times 2.94 \).
\( \frac{1}{2} \times 1.17 \times 2.94 = 0.5 \times 1.17 \times 2.94 = 0.5 \times 3.4398 = 1.7199 \) square units.

Step2: Find total area of circle (16 sectors)

Since there are 16 congruent sectors, total area of circle is \( 16 \times \) area of one sector. So, \( 16 \times 1.7199 = 27.5184 \approx 27.52 \) square units.

Answer:

27.52 units² (corresponding to the option with 27.52 units²)