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Let's do this question, a quadrilaterals formed by joining the midpoint of two sides of an equilateral

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triangle, the sock'em radius of the equilateral triangle is 15 centimeter.

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Find the area of the quadrilateral formed.

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All right.

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Pause the video, give it a try and then let's do it together.

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All right, we're back.

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I hope you've given it a try.

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Let's do it together.

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Now, we have an equilateral triangle over here and it's mentioned that a quadrilateral is formed by

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joining the midpoint of two sites, which we have done that over here.

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And we get a quadrilateral over here.

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Remember, a quadrilateral is a four sided polygon.

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All right.

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Now, let the side length of this equilateral triangle be OK.

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And it's mentioned that the Zakim radius of the equilateral triangle is equal to 15 centimeter.

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All right.

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Now, we know that in an equilateral triangle, the sock'em radius is equal to two by three.

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The height of the equilateral triangle.

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Right.

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OK, so using this, we can find out that each is equal to 15 to three by two, that's equal to forty

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five by two centimeter.

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And we know that in an eternal triangle, it is also equal to room three by two eight.

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Right.

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Rule three by two.

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It is the side, the four by four divided by two is equal to rule three by two eight.

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And we can find that is equal to forty five by rule three, which is also equal to 15.

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Rule three.

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All right.

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Now we know that the area of the equilateral triangle is equal to room three by four is square.

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That's rule three by four in two 15 square into three.

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Right.

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Because we are taking 15, rule three, the square and that's equal to six seventy five, rule three

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by four.

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So this is the area of this triangle.

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Now I can divide this equilateral triangle into four congruent triangles by joining these points.

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Right.

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So I'm getting one, two, three and four or equilateral triangles and they are of equal area.

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They're congruent triangles.

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Let me name these points as per the question.

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I need to find the area of quadrilateral ABCDE.

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Right.

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And that would be taking three parts out of four equal parts.

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Right.

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So this area has been divided into four equal parts.

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And I just need to take three parts to the area of Quarrell.

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ABC will be equal to three by four.

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The area of the equilateral triangle, that is three by four and two six seventy five rule three by

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four, because that's what we found over here.

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And this is equal to two thousand twenty five, rule three by sixteen, which is your answer.

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Let's quickly revise what is the approach that we followed?

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We started identifying the saken radius as two by three inch and it is also equal to rule three by two

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eight.

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So we equated these two and we found this side of the equilateral triangle.

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After finding the side, we were able to find the area using the formula rule three by four square.

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And then we have observed that this quadrilateral over here is taking three four the area of the.

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Equilateral triangle.

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And using this, we have found the area of the quadrilaterals.