Question

10 POINTS AND BRAINLIEST FOR CORRECT ANSWER

Answer 1

Area of semicircle = 4pi
Area of Triangle = 8
Area of Shaded Region= 4pi-8

Answer 2

Answer:

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:

$LN^2=4^2+4^2\\\\LN^2=16+16\\\\LN^2=32\\\\LN=\sqrt{32}\\\\LN=4\sqrt{2}$

Hence, Area of triangle is:

$\dfrac{1}{2}\times {MN}\times {LM}\\\\=\dfrac{1}{2}\times 4\times 4\\\\=8 cm^2$

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

Hence, Radius of circle=2√2 cm.

Area of semicircle is given by:

$\dfrac{\pi r^2}{2}\\\\=\dfrac{1}{2}\times \pi\times 2\sqrt{2}\times 2\sqrt{2}\\\\=4\pi cm^2$

Hence, Area of shaded region is:

(4π-8) cm^2