Final answer:
To approximate the area of the circle, calculate the area of one sector using the triangle area formula (1/2 × base × height) and then multiply by the number of sectors. The correct answer is b) 27.52 units².
Step-by-step explanation:
The question asks to find the approximate area of the circle using the given dimensions of one of its congruent sectors.
Since the circle is divided into 16 congruent sectors, each sector is essentially a triangle with a base of 1.17 units and a height of 2.94 units. We can use the area of a triangle formula, which is 1/2 × base × height.
First, we calculate the area of one sector: Area = 1/2 × 1.17 units × 2.94 units = 1.7229 units². Since there are 16 sectors, we multiply the area of one sector by 16 to get the total area of the circle, yielding 27.5264 units²,
which is approximately 27.52 units² when rounded to two decimal places. Therefore, the correct answer is b) 27.52 units².