Question

What is the area of the half circle below?2 Pi 4pi 8pi 16pi

Answer 1

Answer:

The area of semicircle is 8π cm².

Step-by-step explanation:

$\large{\tt{\underline{\underline{\red{SOLUTION}}}}}$

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 :

${\longrightarrow{\pmb{\sf{Area_{(Semicircle)} = \dfrac{1}{2}( \pi {r}^{2})}}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(4)}^{2}\Big)}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(4 \times 4)}\Big)}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi {(16)}\Big)}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\Big( \pi \times 16\Big)}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2}\big( 16\pi \big)}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{2} \times 16\pi}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = \dfrac{1}{\cancel{2}} \times \cancel{16}\pi}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = 1 \times 8\pi}}}$

${\longrightarrow{\sf{Area_{(Semicircle)} = 8\pi}}}$

$\star{\underline{\boxed{\sf{ \purple{Area_{(Semicircle)} = 8\pi \: cm^2}}}}}$

Hence, the area of semicircle is 8π cm².

$\rule{300}{2.5}$

Answer 2

Answer:

A = 8π cm²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Here diameter = 8 , then r = 8 ÷ 2 = 4

The area of half a circle is then

A = $\frac{1}{2}$ π × 4² = $\frac{1}{2}$ × π × 16 = 8π cm²