Let's do this question, a quadrilaterals formed by joining the midpoint of two sides of an equilateral
triangle, the sock'em radius of the equilateral triangle is 15 centimeter.
Find the area of the quadrilateral formed.
All right.
Pause the video, give it a try and then let's do it together.
All right, we're back.
I hope you've given it a try.
Let's do it together.
Now, we have an equilateral triangle over here and it's mentioned that a quadrilateral is formed by
joining the midpoint of two sites, which we have done that over here.
And we get a quadrilateral over here.
Remember, a quadrilateral is a four sided polygon.
All right.
Now, let the side length of this equilateral triangle be OK.
And it's mentioned that the Zakim radius of the equilateral triangle is equal to 15 centimeter.
All right.
Now, we know that in an equilateral triangle, the sock'em radius is equal to two by three.
The height of the equilateral triangle.
Right.
OK, so using this, we can find out that each is equal to 15 to three by two, that's equal to forty
five by two centimeter.
And we know that in an eternal triangle, it is also equal to room three by two eight.
Right.
Rule three by two.
It is the side, the four by four divided by two is equal to rule three by two eight.
And we can find that is equal to forty five by rule three, which is also equal to 15.
Rule three.
All right.
Now we know that the area of the equilateral triangle is equal to room three by four is square.
That's rule three by four in two 15 square into three.
Right.
Because we are taking 15, rule three, the square and that's equal to six seventy five, rule three
by four.
So this is the area of this triangle.
Now I can divide this equilateral triangle into four congruent triangles by joining these points.
Right.
So I'm getting one, two, three and four or equilateral triangles and they are of equal area.
They're congruent triangles.
Let me name these points as per the question.
I need to find the area of quadrilateral ABCDE.
Right.
And that would be taking three parts out of four equal parts.
Right.
So this area has been divided into four equal parts.
And I just need to take three parts to the area of Quarrell.
ABC will be equal to three by four.
The area of the equilateral triangle, that is three by four and two six seventy five rule three by
four, because that's what we found over here.
And this is equal to two thousand twenty five, rule three by sixteen, which is your answer.
Let's quickly revise what is the approach that we followed?
We started identifying the saken radius as two by three inch and it is also equal to rule three by two
eight.
So we equated these two and we found this side of the equilateral triangle.
After finding the side, we were able to find the area using the formula rule three by four square.
And then we have observed that this quadrilateral over here is taking three four the area of the.
Equilateral triangle.
And using this, we have found the area of the quadrilaterals.