Question

55. Find the area of half of a circle with a radius of 16 mm.

Give your answer correct to three decimal places.

Answer 1

`\huge \green{\underbrace{ \red{\rm \: Answer}}}`

To find the area of this square, we have to figure out what to do with given radius

r=16r=16 mm.

Radius makes half of the square's diagonal, therefore: d=2r=32d=2r=32 mm. Now we have to find the side aa to find the area.

To find aa, use the Pythagorean Theorem.

`d^(2)&=a^(2)+a^(2) \\ 32^(2)&=2a^(2)\\ 1024&=2a^(2)\\ 512\text{ mm}^(2)&=a^(2)a^(2)`

Set the equation accordingly.

Substitute for d.

You can keep a2 as we will use it in the area.

`\textbf{Finding the area} \\A=a^(2) \\A=512\text{ mm}^(2)`

Thankyou :D