Question

1 what is the best estimate of the area of the figure below? 4 in 6 in

Explanation:

Step1: Calculate area of rectangle

The rectangle has length $6$ in and height $4$ in. Area of a rectangle is $\text{length} \times \text{height}$.
$\text{Area}_{\text{rectangle}} = 6 \times 4 = 24$ in$^2$

Step2: Calculate area of semicircle

The semicircle has a diameter equal to the rectangle's length ($6$ in), so radius $r = \frac{6}{2} = 3$ in. Area of a semicircle is $\frac{1}{2} \pi r^2$.
$\text{Area}_{\text{semicircle}} = \frac{1}{2} \times \pi \times 3^2 = \frac{1}{2} \times \pi \times 9 = 4.5\pi \approx 14.13$ in$^2$

Step3: Sum the two areas

Add the area of the rectangle and semicircle to get total area.
$\text{Total Area} = 24 + 14.13 = 38.13$ in$^2$

Answer:

The best estimate of the area is approximately $\boldsymbol{38}$ square inches (or $\boldsymbol{24 + 4.5\pi}$ square inches for the exact value).