Question

Mr. Martinez wants to make name tags in the shape of sneakers for participants in the jog-a-thon, using the design shown below

Answer 1

The shape of the sneaker is figure compounded by many geometric forms. To determine the area we have to identify each form and use the appropriate formula for that part and sum it all up in the end. The forms are shown below:

The three forms are a rectangle, on the left, a trapezoid on the middle and a semicircle on the right. The formula to calculate the area of each of these figures are shown below:

`\begin{gathered} \text{ Rectangle=}b\cdot h \\ \text{ Trapezoid}=((B+b)\cdot h)/(2) \\ \text{Semicircle=}(\pi\cdot r^2)/(2) \end{gathered}`

Now we can use the data from the problem to calculate the areas

`\begin{gathered} \text{ Rectangle}=3\cdot5=15\text{ square centimeters} \\ \text{ Trapezoid}=((6+4)\cdot4)/(2)=20\text{ square centimeters} \\ \text{ Semicircle}=(\pi\cdot(2)^2)/(2)=6.28\text{ square centimeters} \end{gathered}`

Now we need to add the three areas to obtain the area of the sneaker.

`\text{Area}=15+20+6.28=41.28\text{ square centimeters}`