Question

due friday februa rectangle, a triangle, and two congruent semicircles were used to form the figure shown.which measurement is closest to the area of the figure in square centimeters?f $67\\ \text{cm}^2$g $74\\ \text{cm}^2$h $79\\ \text{cm}^2$j $88\\ \text{cm}^2$

Explanation:

Step1: Calculate triangle area

$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2$

Step2: Calculate rectangle area

$\text{Area}_{\text{rectangle}} = 8 \times 6 = 48 \, \text{cm}^2$

Step3: Calculate semicircles area

Two congruent semicircles form one full circle. Radius $r = \frac{3}{2} = 1.5 \, \text{cm}$.
$\text{Area}_{\text{circles}} = \pi r^2 = \pi (1.5)^2 = 2.25\pi \approx 7.07 \, \text{cm}^2$

Step4: Sum all areas

$\text{Total Area} = 12 + 48 + 7.07 = 67.07 \, \text{cm}^2$

Answer:

F $67 \, \text{cm}^2$