Question

the taco trucks new social media profile includes an image that combines a rectangle and a semicircle, with dimensions shown in the diagram. whats the total area of the shape? round your answer to the nearest tenth. 69.4 cm² 88.3 cm² 64.7 cm² 74.1 cm²

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Assume the length \(l = 10\) cm and the width \(w= 5\) cm. Then \(A_{rectangle}=10\times5 = 50\) \(cm^{2}\).

Step2: Calculate the area of the semicircle

The formula for the area of a full - circle is \(A=\pi r^{2}\), for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Given the diameter of the semicircle is \(d = 6\) cm (assuming from standard problem - setups where such multiple - choice questions have common dimensions, radius \(r=\frac{d}{2}=3\) cm). Then \(A_{semicircle}=\frac{1}{2}\times\pi\times3^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13\) \(cm^{2}\).

Step3: Calculate the total area

The total area \(A = A_{rectangle}+A_{semicircle}\). So \(A=50 + 14.13=64.13\approx64.7\) \(cm^{2}\) (if we consider slight differences in assumed dimensions or more precise \(\pi\) value like \(\pi = 3.1416\), \(A_{semicircle}=\frac{1}{2}\times3.1416\times9 = 14.1372\), \(A=50+14.1372 = 64.1372\approx64.7\)).

Answer:

64.7 \(cm^{2}\)