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Aleks [24]
2 years ago
5

Find the perimeter of a parallelogram and one semicircle

Mathematics
1 answer:
ch4aika [34]2 years ago
7 0

Answer:

  1. For semicircle examples, skip to section 1
  2. For parallelogram examples, skip to section 2

To find the perimeter of a parallelogram, use the formula, 2(a+b)

To find a semicircle perimeter, use the formula of (π × r) + (2 × r)

<em>note that without any specified values for the shapes, you cannot properly find a value.</em>

__________

1. \sf Semicircles

So let's say I have a bowl that is ironically shaped like a semicircle, and its radius is 6 units.

  • What we know is that the semicircle has a radius of 8 units, and what we must find is the perimeter.
  • So let's solve.

Use the formula from earlier.(Using 3.14 for pi)

(\pi *r)+(2*r)

=\pi * r(8) + 2 * r(8) = 41.12

__________

2. \sf Parallelograms

And let's say I have a new origami shape that contains a figure similar to a parallelogram. We want to find it's perimeter. What is the first step?

  • The first step is using the parallelogram perimeter formula as listed below and above.

2(a+b)

Where <em>a</em> is the side and <em>b</em> is the base.

  • And let's also say this figure has a base of 7 and a side of... let's say a side length of 9
  • Now that we have values, use the formula to solve.

2*(7+9) = 32

__________

\sf Questions

If you have any questions, please reach out via the comments. I hope this helps, and have a great day!

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\huge\bold{Given:}

Length of the base = 16 km.

Length of the hypotenuse = 34 km. \huge\bold{To\:find:}

✎ The length of the missing leg ''a".

\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}

The length of the missing leg "a" is\boxed{30\:km}.

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}

Using Pythagoras theorem, we have

({perpendicular})^{2}  +  ({base})^{2}  =  ({hypotenuse})^{2}  \\ ⇢ {a}^{2}  +  ({16 \: km})^{2}  =  ({34 \: km})^{2}  \\ ⇢ {a}^{2}   + 256 \:  {km}^{2}  = 1156 \:  {km}^{2}  \\ ⇢ {a}^{2}  = 1156 \:  {km}^{2}  - 256 \:  {km}^{2}  \\ ⇢ {a}^{2}  = 900 \:  {km}^{2}  \\ ⇢a \:  =  \sqrt{900  \: {km}^{2} }  \\ ⇢a =  \sqrt{30 \times 30 \:  {km}^{2} }  \\ ⇢a = 30 \: km

\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:leg\:"a"\:is\:30\:km.}

\huge\bold{To\:verify :}

( {30 \: km})^{2}  +  ({16 \: km})^{2}  =(  {34 \: km})^{2}  \\ ⇝900 \:  {km}^{2}  + 256 \:  {km}^{2}  = 1156 \:  {km}^{2}  \\⇝1156 \:  {km}^{2}  = 1156 \:  {km}^{2}   \\ ⇝L.H.S.=R. H. S

Hence verified. ✔

\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘

7 0
2 years ago
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