Question

##15 points#### In the given figure triangle ABC is an equilateral triangle inscribed in a circle of radius 4 cm. find the area of shaded region.

Answer 1

here is your answer
you are given radius = 4cm ..

therefore we know that area of a semicircle =
pie×radius square ÷2

also the shaded area is a semicircle

so area of the semicircle = pie ×radius square ÷2
= 3.14×4×4÷2
= 25.12cm square ..

theirfore,,the required area = 25.12 cm square

Answer 2

here is your answer. area of all the 3 semi elliptical portions is equal. when you draw an equilateral triangle inside a circle, 3 semi-elliptical segments of equal area are left out.
now, area of the circle is 16π.
according to the picture, O is the center of the circle, as well as the centroid of the triangle. now BO =4 cm. so OD = 2 cm. therefore the height of the triangle is 4+2= 6 cm. calculate BE from triangle OBE using Pythagoras's theorem. base of ABC , BC=2*BE. calculate the area of ABC from 1/2*base*height formula. subtract it from 16π and divide it by 3, and you got the area of the shaded portion. I've added a photo for your convenience.