Question

In the above attatchment,

The quadrilateral is a square with sides 10m.Find the area of the shaded red portion.

◇Please do it with full explanation and in detail.​

Answer 1

Answer:

Given, side is 10m.

The semi-circle on the left (smaller one) has diameter too of 10m

Hence its radius is 5m

It's area will be half the area of full circle of radius 5m.

=> Area_1A = 78.5/2

= 39.25 sqm

Note that the topmost semi-circle will also have the same area since it also has the same diameter, so let it be Area_1B.

Now, for the left most bigger semi-circle, it's actually a half of a semi-circle. If you draw a perpendicular line from the center of a semi-circle, it divides into two quadrants.

So, this quadrant has radius 10m now (both sides of a quadrant are the radius of the actual circle).

Hence its area will be the quarter of the actual circle's area.

=> Area_2 = 314/4

= 78.50 sqm

Now we have all the data we need to proceed finding the shaded area.

Let the shaded area be y sqm.

Let the unshaded portion of the topmost semi-circle be x and z sqm.

Hence,

x+y+z = Area_1B = 39.25 sqm

=> y = 39.25-x-z

Frankly speaking, there are too many unknowns now to proceed with the question, according to me. If x and z are known (by integration probably, which I don't know much about it), you can find that shaded portion area.

Hope this helped.