Question

the area of the figure shown below is ______ cm². (round to the nearest cm²)
(hint: the area of a square is found by ( s^2 ) and the area of a circle by ( pi r^2 ))
select one:
a. ( 573 , \text{cm}^2 )
b. ( 324 , \text{cm}^2 )
c. ( 254 , \text{cm}^2 )
d. ( 70 , \text{cm}^2 )
e. ( 81 , \text{cm}^2 )

a circle has a diameter of 24 cm
what is the area of the circle?

Explanation:

Step1: Calculate square area

The square has side length $s=18$ cm. Area formula: $s^2$.
$\text{Area}_{\text{square}} = 18^2 = 324$ $\text{cm}^2$

Step2: Calculate full circle area

The two semicircles form one full circle with diameter equal to the square's side ($18$ cm), so radius $r=\frac{18}{2}=9$ cm. Area formula: $\pi r^2$.
$\text{Area}_{\text{circle}} = \pi \times 9^2 = 81\pi \approx 254$ $\text{cm}^2$

Step3: Sum the two areas

Add the square and circle areas to get total figure area.
$\text{Total Area} = 324 + 254 = 578$ $\text{cm}^2$

Step1: Find the circle's radius

Radius is half the diameter.
$r = \frac{24}{2} = 12$ cm

Step2: Calculate the circle's area

Use the circle area formula $\pi r^2$.
$\text{Area} = \pi \times 12^2 = 144\pi \approx 452$ $\text{cm}^2$

Answer:

a. 578 cm²

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For the additional circle question (diameter 24 cm):