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# Help with (b) I halfway got it correct but I think I am calculating it wrong. :/

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Help with (b) I halfway got it correct but I think I am calculating it wrong. :/

Sep 23, 2018

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a)

Since these are composite figures, it is probably best to think about each composite figure as each individual shape that it is comprised of. Let's first discern the perimeter of the trapezoid.

We know three of the four sides, and the fourth side is of equal length to its opposite side. The fourth side is not exposed, so we can ignore it from the calculation. Just add these lengths together to obtain the perimeter. Multiply this perimeter by two because there are two trapezoids in this diagram.

$$P_{\text{trpzd}}=(13+9+7)\text{mm}\\ P_{\text{trpzd}}=29\text{mm}\\ 2P_{\text{trpzd}}=58\text{mm}$$

The only length left to determine is the arc length of the circular arc. The circumference of the circle is $$C=2\pi r$$, but we only want 44 of the 360 degrees of the circle. Add these perimeters together to find the final perimeter.

$$\text{Arclength}=2\pi r*\frac{44}{360}; r=9\text{mm}\\ \text{Arclength}=\frac{99\pi}{45}\text{mm}\approx6.9115\text{mm}$$

Add these perimeters together to find the final perimeter:

$$2P_{\text{trpzd}}+\text{Arclength}=58\text{mm}+6.9115\text{mm}\\ 2P_{\text{trpzd}}+\text{Arclength}=64.9115\text{mm}\approx64.91\text{mm}$$

And that's that!

b)

The base of the equilateral triangle is 7cm. The collinear radii of the circular arc are also 7cm.  This means that

$$P_{\triangle\text{ & radii}}=(7+7+7)\text{cm}\\ P_{\triangle\text{ & radii}}=21\text{cm}$$

The only thing left to do is find the arc length, just like the previous problem. There are two arcs this time. Make sure to take that into account.

$$\text{Arclength}=2\pi r*\frac{120}{360}; r=7\text{cm}\\ \text{Arclength}=\frac{14\pi}{3}\text{cm}\\ 2\text{Arclength}=\frac{28\pi}{3}\text{cm}\approx29.3215\text{cm}$$

Find the sum of these perimeters again:

$$P_{\triangle\text{ & radii}}+\text{Arclength}=21\text{cm}+29.3215\text{cm}\\ P_{\triangle\text{ & radii}}+\text{Arclength}=50.3215\text{cm}\approx50.32\text{cm}$$

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Sep 24, 2018