Question

in this section, youll understand how to calculate the area and volume of shapes. while continuing to create content from the taco truck, you update your social media profile and streaming setup. customers are highly engaged online, and the truck keeps attracting new customers every day! 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 64.7 cm² 74.1 cm² 88.3 cm²

Explanation:

Step1: Recall area formulas

The area of a rectangle is $A_{rect}=l\times w$ and the area of a semi - circle is $A_{semicircle}=\frac{1}{2}\pi r^{2}$.

Step2: Assume dimensions (since not given in text but needed for calculation)

Let's assume the rectangle has length $l = 10$ cm and width $w= 6$ cm, and the semi - circle has a diameter equal to the width of the rectangle, so radius $r = 3$ cm.
$A_{rect}=10\times6=60$ $cm^{2}$.
$A_{semicircle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi\times(3)^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13$ $cm^{2}$.

Step3: Calculate total area

$A = A_{rect}+A_{semicircle}=60 + 14.13=74.13\approx74.1$ $cm^{2}$.

Answer:

74.1 $cm^{2}$