Answer:
The area of semicircle is 8π cm².
Step-by-step explanation:
[tex]\large{\tt{\underline{\underline{\red{SOLUTION}}}}}[/tex]
Given :
Here we have given that the diameter of a semicircle is 8 cm. So, the radius will be 8/2 = 4 cm.
Calculating :
Now, finding the area of semicircle by substituting the values in the formula :
[tex]{\longrightarrow{\pmb{\sf{Area_{(Semicircle)} = \dfrac{1}{2}( \pi {r}^{2})}}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(4)}^{2}\Big)}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(4 \times 4)}\Big)}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(16)}\Big)}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi \times 16\Big)}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\big( 16\pi \big)}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2} \times 16\pi}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{\cancel{2}} \times \cancel{16}\pi}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = 1 \times 8\pi}}}[/tex]
[tex]{\longrightarrow{\sf{Area_{(Semicircle)} = 8\pi}}}[/tex]
[tex]\star{\underline{\boxed{\sf{ \purple{Area_{(Semicircle)} = 8\pi \: cm^2}}}}}[/tex]
Hence, the area of semicircle is 8π cm².
[tex]\rule{300}{2.5}[/tex]