Question

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. 2 un 2 un 3 un what is the area of the shaded part of the figure shown? use 3 for π.

Explanation:

Step1: Calculate area of quarter circle

The radius of the quarter circle is 3 units, and we use $\pi=3$.
Area formula: $\frac{1}{4} \pi r^2$
$\frac{1}{4} \times 3 \times 3^2 = \frac{1}{4} \times 3 \times 9 = \frac{27}{4} = 6.75$ square units

Step2: Calculate area of square

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

Step3: Calculate area of unshaded triangle

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

Step4: Find total shaded area

Shaded area = (Area of quarter circle - Area of square) + Area of shaded triangle
$(6.75 - 4) + 2 = 2.75 + 2 = 4.75$ square units, or $\frac{19}{4}$ square units

Answer:

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