Question

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

Answer 1

The area of semicircle is 537.82 cm².

Step-by-step Step-by-step explanation:

Given :

• Diameter of semicircle = 37 cm.

To Find :

• Area of semicircle

Using Formula :

`{\star{\small{\underline{\boxed{\sf{\red{R = (D)/(2)}}}}}}}`

• R = Radius
• D = Diameter

`{\star{\small{\underline{\boxed{\sf{\red{Area = (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 = (D)/(2)}}}}`

`{\dashrightarrow{\sf{Radius = (37)/(2)}}}`

`{\dashrightarrow{\sf{Radius = \cancel{(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 = (1)/(2)\pi{r}^(2)}}}}`

`{\longrightarrow{\sf{Area = (1)/(2) * (22)/(7) * {(18.5)}^(2)}}}`

`{\longrightarrow{\sf{Area = \frac{1}{\cancel{2}} * \frac{\cancel{22}}{7} * {(18.5 * 18.5)}}}}`

`{\longrightarrow{\sf{Area = (11)/(7) * {(18.5 * 18.5)}}}}`

`{\longrightarrow{\sf{Area = (11)/(7) * {(342.25)}}}}`

`{\longrightarrow{\sf{Area = (11)/(7) * 342.25}}}`

`{\longrightarrow{\sf{Area = (11 * 342.25)/(7)}}}`

`{\longrightarrow{\sf{Area = (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}`