Answer:
A. 4.26 in^2
Step-by-step explanation:
Step 1: Find the area of the sector DBC. Here we have to use the formula.
Area of a sector = Central Angle/360 *π![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
The area of the sector DBC = (54/360)*3.14*![8^{2}](https://tex.z-dn.net/?f=8%5E%7B2%7D)
= 30.16
Step 2: Area of segment CFD = Area of the sector DBC - Area of the ΔCBD
= 30.17 - 25.9
Area of segment CFD = 4.27in^2
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
<h3>How to find the missing side of a right triangle</h3>
In this question we know the lengths of two sides of the <em>right</em> triangle. By Pythagorean theorem we get the length of the missing side:
a² + b² = c²
b² = c² - a²
b = √(c² - a²)
b = √(37² - 12²)
b = 35
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
To learn more on Pythagorean theorem: brainly.com/question/26183488
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