Question

Find the area of this semi-circle with diameter, d = 37cm.
Give your answer rounded to 2 DP.

Answer 1

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 :

${\star{\small{\underline{\boxed{\sf{\red{R = \dfrac{D}{2}}}}}}}}$

• R = Radius
• D = Diameter

${\star{\small{\underline{\boxed{\sf{\red{Area = \dfrac{1}{2}\pi{r}^{2}}}}}}}}$

• 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 :

${\dashrightarrow{\pmb{\sf{Radius = \dfrac{D}{2}}}}}$

${\dashrightarrow{\sf{Radius = \dfrac{37}{2}}}}$

${\dashrightarrow{\sf{Radius = \cancel{\dfrac{37}{2}}}}}$

${\dashrightarrow{\sf{Radius =18.5 \: cm}}}$

${\star{\underline{\boxed{\sf{\pink{Radius =18.5 \: cm}}}}}}$

Hence, the radius of semicircle is 18.5 cm.

$\rule{300}{1.5}$

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

${\longrightarrow{\pmb{\sf{Area = \dfrac{1}{2}\pi{r}^{2}}}}}$

${\longrightarrow{\sf{Area = \dfrac{1}{2} \times \dfrac{22}{7} \times {(18.5)}^{2}}}}$

${\longrightarrow{\sf{Area = \dfrac{1}{\cancel{2}} \times \dfrac{\cancel{22}}{7} \times {(18.5 \times 18.5)}}}}$

${\longrightarrow{\sf{Area = \dfrac{11}{7} \times {(18.5 \times 18.5)}}}}$

${\longrightarrow{\sf{Area = \dfrac{11}{7} \times {(342.25)}}}}$

${\longrightarrow{\sf{Area = \dfrac{11}{7} \times 342.25}}}$

${\longrightarrow{\sf{Area = \dfrac{11 \times 342.25}{7}}}}$

${\longrightarrow{\sf{Area = \dfrac{3764.75}{7}}}}$

${\longrightarrow{\sf{Area \approx 537.82 \: {cm}^{2}}}}$

${\star{\underline{\boxed{\sf{\pink{Area \approx 537.82 \: {cm}^{2}}}}}}}$

Hence, the area of semicircle is 537.82 cm².

$\rule{300}{1.5}$