Question

Find the area and perimeter of the shaded region.

Answer 1

Perimeter- 20
Area- 50-100

Answer 2

Area:
`50\pi -100`

Perimeter: 20
`\pi`

Explanation:

If we take half of one of these "pedals" we can see that it is simply 1/4 of a circle with radius 5, subtracted by a triangle. Let's calculate this half-pedal.

`1/4(25 \pi) - 1/2(5* 5)`

That means 4 pedals is equal to:

`8(1/4(25\pi) - 1/2 (25))`

`50\pi - 100`

So.. The area of the shaded region is
`50\pi -100`

Perimeter is even simpler. the half-pedal is just 1/4 of the circumference of the circle. The circumference is just
`10\pi`, which means our half pedal is:

`1/4(10\pi )`

Multiplying by 8, our perimeter is just 20
`\pi`.