Question

elay race problems
2.) samuel placed a quarter circle tile on a table. on top of that he placed a square tile and then a triangle to form the shape below with the given dimensions.
what is the area of the shaded part of the figure shown? use 3 for $pi$.

Explanation:

Step1: Calculate quarter circle area

The radius of the quarter circle is 3 units. Area of a full circle is $\pi r^2$, so quarter circle area is $\frac{1}{4} \pi r^2$. Using $\pi=3$:
$\frac{1}{4} \times 3 \times 3^2 = \frac{1}{4} \times 3 \times 9 = \frac{27}{4} = 6.75$ square units

Step2: Calculate square area

The square has side length 2 units. Area of square is $s^2$:
$2^2 = 4$ square units

Step3: Calculate unshaded triangle area

The triangle has base 2 units and height 2 units. Area of triangle is $\frac{1}{2} \times b \times h$:
$\frac{1}{2} \times 2 \times 2 = 2$ square units

Step4: Find shaded area

Shaded area = (Quarter circle area - Square area) + (Square area - Triangle area)
Alternatively, simplify to: Quarter circle area - Triangle area
$6.75 - 2 = 4.75$ square units (or $\frac{19}{4}$ square units)

Answer:

$\frac{19}{4}$ square units (or 4.75 square units)