Mathematics, 13.03.2022 15:50 dudesenpai24

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

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Answer from: punani

Answer:8.78 cmSolution:

We are given that :

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

Using Formulas:

Area of rectangle:

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

Area of semicircle:

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

We have to find the length of longer side of rectangle!

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 ;

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

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

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

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

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

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

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

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

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

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

Answer from: Quest

is there answer choices?

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangl...

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