Question

Find the area and perimeter of the shaded region.

Answer 1

Perimeter- 20
Area- 50-100

Answer 2

Answer:

Area: $50\pi -100$

Perimeter: 20$\pi$

Step-by-step 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$\pi$.