Question

unit 1 summative (area/perimeter/volume/surface area a square has side length 14 cm. a semicircle is attached to one side of the square. find the area of the composite figure. (round to nearest whole number) 273 cm² 246 cm² 258 cm² 308 cm²

Explanation:

Step1: Calculate area of square

The area of a square is given by the formula \( A_{square} = s^2 \), where \( s \) is the side length. Here, \( s = 14 \) cm. So, \( A_{square} = 14^2 = 196 \) \( cm^2 \).

Step2: Calculate area of semicircle

The diameter of the semicircle is equal to the side length of the square, so \( d = 14 \) cm, which means the radius \( r = \frac{d}{2} = \frac{14}{2} = 7 \) cm. The area of a full circle is \( A_{circle} = \pi r^2 \), so the area of a semicircle is \( A_{semicircle} = \frac{1}{2} \pi r^2 \). Substituting \( r = 7 \) cm, we get \( A_{semicircle} = \frac{1}{2} \times \pi \times 7^2 = \frac{1}{2} \times \pi \times 49 \approx \frac{1}{2} \times 3.1416 \times 49 \approx 76.969 \) \( cm^2 \).

Step3: Calculate area of composite figure

The area of the composite figure is the sum of the area of the square and the area of the semicircle. So, \( A_{composite} = A_{square} + A_{semicircle} = 196 + 76.969 \approx 272.969 \), which rounds to 273 \( cm^2 \).

Answer:

273 \( cm^2 \) (corresponding to the option "273 \( cm^2 \)")