10 points and brainliest for correct answer

find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

Hence, Area of shaded region is:

(4π-8) cm^2

Step-by-step explanation:

We are asked to find the area of the shaded region.

we could clearly observe that:

Area of shaded region=Area of semicircle-Area of right triangle.

As we are given two angles of a triangle so the third angle is equal to 45°.

We could find the length of the side with the help of the trignometric formula as:

tan 45=MN/LM

1=MN/4

MN=4 cm

Similarly we can find the side LN with the help of the Pythagorean theorem as:

Hence, Area of triangle is:

similarly we have diameter of semicircle=4√2 cm.

Hence, Radius of circle=2√2 cm.

Area of semicircle is given by:

Hence, Area of shaded region is:

(4π-8) cm^2

14

step-by-step explanation: