Find the Area in the square but outside the circle. 2. Calculate the area and circumference of the circle shown below. Use pi = 3.14. 3. Calculate the area and circumference of the circle shown below. Use pi = 3.14. 4. Calculate the perimeter. Give your answer to 1 decimal place.

The area of a square is given by $A_{square} = side^2$.

$$A_{square} = (8 \text{ cm})^2$$ $$A_{square} = 64 \text{ cm}^2$$

The area of a circle is given by $A_{circle} = \pi r^2$.

$$A_{circle} = \pi (4 \text{ cm})^2$$ $$A_{circle} = 16\pi \text{ cm}^2$$

Using $\pi \approx 3.14159$:

$$A_{circle} \approx 16 \times 3.14159 \text{ cm}^2$$ $$A_{circle} \approx 50.265 \text{ cm}^2$$

This area is the difference between the area of the square and the area of the circle.

$$A_{difference} = A_{square} - A_{circle}$$ $$A_{difference} = 64 \text{ cm}^2 - 16\pi \text{ cm}^2$$ $$A_{difference} \approx 64 \text{ cm}^2 - 50.265 \text{ cm}^2$$ $$A_{difference} \approx 13.735 \text{ cm}^2$$

Answer: 13.735 cm^2 (approx.) or (64 - 16\pi) cm^2

Q2. Calculate the area and circumference of the circle shown below. use $\pi = 3.14$
The diagram shows a circle with a radius ($r$) of $4.5 \text{ ft}$.

The area of a circle is $A = \pi r^2$.

$$A = 3.14 \times (4.5 \text{ ft})^2$$ $$A = 3.14 \times 20.25 \text{ ft}^2$$ $$A = 63.585 \text{ ft}^2$$

The circumference of a circle is $C = 2\pi r$.

$$C = 2 \times 3.14 \times 4.5 \text{ ft}$$ $$C = 6.28 \times 4.5 \text{ ft}$$ $$C = 28.26 \text{ ft}$$

Answer: Area = 63.585 ft^2, Circumference = 28.26 ft

Q3. Calculate the area and circumference of the circle shown below. use $\pi = 3.14$
The diagram shows a circle with a diameter ($d$) of $14 \text{ in}$. The radius ($r$) is half of the diameter, so $r = \frac{14}{2} = 7 \text{ in}$.

The area of a circle is $A = \pi r^2$.

$$A = 3.14 \times (7 \text{ in})^2$$ $$A = 3.14 \times 49 \text{ in}^2$$ $$A = 153.86 \text{ in}^2$$

The circumference of a circle is $C = \pi d$ or $C = 2\pi r$.

$$C = 3.14 \times 14 \text{ in}$$ $$C = 43.96 \text{ in}$$

Answer: Area = 153.86 in^2, Circumference = 43.96 in

Q4. Calculate the perimeter. Give your answer to 1 decimal place.
The diagram shows a semicircle with a diameter ($d$) of $4 \text{ cm}$. The radius ($r$) is half of the diameter, so $r = \frac{4}{2} = 2 \text{ cm}$.
The perimeter of a semicircle includes the curved arc length and the straight diameter.

The arc length of a semicircle is half the circumference of a full circle: $\frac{1}{2} (2\pi r) = \pi r$.

$$Arc\ Length = \pi \times 2 \text{ cm}$$ $$Arc\ Length = 2\pi \text{ cm}$$

Using $\pi \approx 3.14159$:

$$Arc\ Length \approx 2 \times 3.14159 \text{ cm}$$ $$Arc\ Length \approx 6.28318 \text{ cm}$$

The perimeter is the arc length plus the diameter.

$$Perimeter = Arc\ Length + d$$ $$Perimeter = 2\pi \text{ cm} + 4 \text{ cm}$$ $$Perimeter \approx 6.28318 \text{ cm} + 4 \text{ cm}$$ $$Perimeter \approx 10.28318 \text{ cm}$$

$$Perimeter \approx 10.3 \text{ cm}$$

Answer: 10.3 cm