Find the area of the shaded part of the figure if $a = 5$ , $$b = 3$$ .
A) 34
B) 18
C) 32.5
D) 12
E) none of these

Question

Find the area of the shaded part of the figure if $a = 5$ , $$b = 3$$ . 
A) 34 
B) 18 
C) 32.5 
D) 12 
E) none of these

Quizplus · Accepted Answer

To find the area of the shaded part, we need to subtract the area of the triangle from the area of the sector.

First, we find the area of the sector:

The central angle of the sector is 120° (360°/3). The radius is 5. So, the area of the sector is:

$$\frac{120°}{360°} \cdot \pi (5)^2 = \frac{25}{3} \pi$$

Next, we find the area of the triangle:

The base of the triangle is 3, and the height can be found using the Pythagorean theorem:

$$h^2 = 5^2 - 3^2 = 16$$
$$h = 4$$

So, the area of the triangle is:

$$\frac{1}{2} (3)(4) = 6$$

Finally, we can find the area of the shaded part by subtracting the area of the triangle from the area of the sector:

$$\frac{25}{3} \pi - 6 \approx 32.5$$

Therefore, the answer is (C) 32.5.

Find the Area of the Shaded Part of the Figure a=5a = 5a=5