Question

1) Find the circumference and Area

Answer 1

Answer:

See below.

Step-by-step explanation:

1) We know that the circumference of a circle can be found using the formula $c=\pi d$, so for this circle the circumference will be $c=3.14 \times 40=125.6 \text{ yards}$. The formula for the area of a circle is $A=\frac{1}{4}\pi d^2$, so the area of this circle will be $A=\frac{1}{4} \times 3.14 \times 40^2=1256 \text{ yards}$.

2) First we'll work out the length of the curved side of the shape. That's $\frac{1}{2}\times\pi d =\frac{1}{2} \times 3.14 \times 12=18.84 \text{ mm}$. Then, we'll add the length of the other two straight sides to get $10.82 \times 2 + 18.84=40.48 \text{ mm}$. Next: the area of the semi-circle is $\frac{1}{2} \times \frac{1}{4} \pi d^2 = \frac{1}{8} \times 3.14 \times 144 = 56.52 \text{ mm}$. Adding this to the areas of the two triangles: $56.52+2 \times \frac{1}{2}bh=56.52+(\sqrt{10.82^2-9^2)}\times9 \approx 110.57 \text{ to 2 d.p.}$