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lilavasa [31]
2 years ago
10

A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. Th

e area of the figure is 41.4 square centimeters.
What is the length of the longer side of the rectangle?

Use 3.14 for π.

Enter your answer as decimal in the box.
Mathematics
1 answer:
velikii [3]2 years ago
8 0
<h3><u>Answer</u><u>:</u></h3>

  • 8.78 cm
<h3><u>Solution</u><u>:</u></h3>

<em>We are given that :</em>

  • A semicircle is drawn onto the shorter side of rectangle.
  • Shorter side of rectangle measures 4cm. i.e; the diameter of the circle is 4cm
  • Area of the figure is 41.4 cm²

<em><u>Using </u><u>Formulas</u><u>:</u></em>

Area of rectangle:

\quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}

Area of semicircle:

\quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>length </u><u>of </u><u>longer </u><u>side </u><u>of </u><u>rectangle</u><u>!</u>

Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;

\quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}

\quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }

\quad\dashrightarrow\quad \sf {41.4 =  ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }

\quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}

\quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}

\quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}

\quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }

\quad\dashrightarrow\quad \sf { l\times 4 = 35.12}

\quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}

\quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }

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