Question

In the figure below, ABO and GOF are right triangles. How would you represent the area of the shaded region?
1. r^2 (π-1)
2. r^2 (π+1)
2. r^2 (π-1/2)
3. r^2 (1-π)

Answer 1

Answer:

option 1

Step-by-step explanation:

The shaded area is area of circle - area of 2 congruent triangles

area of circle = πr²

Note that the base and height of both triangles is the radius

Area o triangle = $\frac{1}{2}$ ×  r × r = $\frac{1}{2}$r²

area of 2 triangles = 2 × $\frac{1}{2}$ × r² = r²

area of shaded region = πr² - r² = r²(π - 1) → (1)