For 14, we already are given the lengths of every "side" except for one- the curve or the semi-circle's perimeter.
To find the perimeter of the half circle, we simply take the formula for the perimeter of a full circle and divide by two.
This is the formula for the circumference of a circle (circumference is simply the word for perimeter as it pertains to circles):
[tex]c = 2\pi \times r[/tex]
C in the above equation means circumference. r is the radius (the measure between any part on the curve of a circle from the center).
Okay, so now that we got all of that out of the way, we can plug our values in to get what a full perimeter of a circle would be:
[tex]c = 2 \pi \times 9 cm \: \\ c = 18\pi cm[/tex]
For our curve, we want to divide the above in half, since we're dealing with the perimeter of only half a circle.
[tex] \frac{18\pi}{2} \\ \: = approximately \: 28.2743 \: cm[/tex]
Therefore the perimeter of the figure is
[tex]5 + 5 + 12 + 28.2743 \\ = 50.2743 \: (cm)[/tex]
There are approximately 91.44 cm per yard, so:
[tex]50.2743 \div 91.44 = .5498 \: yards[/tex]
Since one yard is worth $27, then we multiply to see how much this figure's perimeter is worth:
[tex].5498 \times 27 \\ = approximately \: 14.85 \: dollars[/tex]
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For 15, we know that we have 6 sides of 3cm so together that's 18cm.
To find the length of the diameter of each semi-circle we take the given lengths of 3cm on each end (there are two) and subtract from the 12cm we are told is the full linear measure. 12- 2*3=6.
Therefore 6cm is the diameter of each semi-circle. We need the radius to find their circumferences, so we divide the diameter in two (since the diameter is two times the length of the radius.
6÷2=3.
Now, to since we have two semi-circles we can just find the circumference of a full circle with these dimensions.
Remember,
[tex]c = 2\pi \times r[/tex]
so, c in our case would be equal to
[tex]c = 2 \pi \times 3cm \\ = 6\pi cm\\ = approximately \: 18.8496 \: cm[/tex]
The 18cm from the other side give us a total perimeter of:
[tex]18 + 18.8496 = 36.8496cm[/tex]
There are 91.44 cm per yard, so
[tex]36.8496 \div 91.44 \\ = approximately.4030 \: yards[/tex]
Since each yard costs $27, then
[tex].4030 \times 27 \\ = approximately \: 10.89 \: dollars[/tex]
