Respuesta :

Answer:

The area of semicircle is 537.82 cm².

Step-by-step explanation:

Given :

  • Diameter of semicircle = 37 cm.

To Find :

  • Area of semicircle

Using Formula :

[tex]{\star{\small{\underline{\boxed{\sf{\red{R = \dfrac{D}{2}}}}}}}}[/tex]

  • R = Radius
  • D = Diameter

[tex]{\star{\small{\underline{\boxed{\sf{\red{Area = \dfrac{1}{2}\pi{r}^{2}}}}}}}}[/tex]

  • π = 22/7
  • r = radius

Solution :

Here we have given that the diameter of semicircle. So, finding the radius of semicircle by substituting the values in the formula :

[tex]{\dashrightarrow{\pmb{\sf{Radius = \dfrac{D}{2}}}}}[/tex]

[tex]{\dashrightarrow{\sf{Radius = \dfrac{37}{2}}}}[/tex]

[tex]{\dashrightarrow{\sf{Radius = \cancel{\dfrac{37}{2}}}}}[/tex]

[tex]{\dashrightarrow{\sf{Radius =18.5 \: cm}}}[/tex]

[tex]{\star{\underline{\boxed{\sf{\pink{Radius =18.5 \: cm}}}}}}[/tex]

Hence, the radius of semicircle is 18.5 cm.

[tex]\rule{300}{1.5}[/tex]

Now, we know the radius of semicircle. Then, finding the area of semicircle by substituting the values in the formula :

[tex]{\longrightarrow{\pmb{\sf{Area = \dfrac{1}{2}\pi{r}^{2}}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{1}{2} \times \dfrac{22}{7} \times {(18.5)}^{2}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{1}{\cancel{2}} \times \dfrac{\cancel{22}}{7} \times {(18.5 \times 18.5)}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{11}{7} \times {(18.5 \times 18.5)}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{11}{7} \times {(342.25)}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{11}{7} \times 342.25}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{11 \times 342.25}{7}}}}[/tex]

[tex]{\longrightarrow{\sf{Area = \dfrac{3764.75}{7}}}}[/tex]

[tex]{\longrightarrow{\sf{Area \approx 537.82 \: {cm}^{2}}}}[/tex]

[tex]{\star{\underline{\boxed{\sf{\pink{Area \approx 537.82 \: {cm}^{2}}}}}}}[/tex]

Hence, the area of semicircle is 537.82 cm².

[tex]\rule{300}{1.5}[/tex]

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